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Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry

Residues and Duality - Lecture Notes of a Seminar on the Work of A. Grothendieck, Given at Harvard 1963 /64 (Paperback, 1966... Residues and Duality - Lecture Notes of a Seminar on the Work of A. Grothendieck, Given at Harvard 1963 /64 (Paperback, 1966 ed.)
Robin Hartshorne
R1,906 Discovery Miles 19 060 Ships in 18 - 22 working days
Moduli Stacks of Etale ( ,  )-Modules and the Existence of Crystalline Lifts - (AMS-215) (Paperback): Matthew Emerton, Toby Gee Moduli Stacks of Etale ( , )-Modules and the Existence of Crystalline Lifts - (AMS-215) (Paperback)
Matthew Emerton, Toby Gee
R1,719 Discovery Miles 17 190 Ships in 10 - 15 working days

A foundational account of a new construction in the p-adic Langlands correspondence Motivated by the p-adic Langlands program, this book constructs stacks that algebraize Mazur's formal deformation rings of local Galois representations. More precisely, it constructs Noetherian formal algebraic stacks over Spf Zp that parameterize etale ( , )-modules; the formal completions of these stacks at points in their special fibres recover the universal deformation rings of local Galois representations. These stacks are then used to show that all mod p representations of the absolute Galois group of a p-adic local field lift to characteristic zero, and indeed admit crystalline lifts. The book explicitly describes the irreducible components of the underlying reduced substacks and discusses the relationship between the geometry of these stacks and the Breuil-Mezard conjecture. Along the way, it proves a number of foundational results in p-adic Hodge theory that may be of independent interest.

Symmetry in Graphs (Hardcover): Ted Dobson, Aleksander Malnic, Dragan Marusic Symmetry in Graphs (Hardcover)
Ted Dobson, Aleksander Malnic, Dragan Marusic
R1,984 Discovery Miles 19 840 Ships in 10 - 15 working days

This is the first full-length book on the major theme of symmetry in graphs. Forming part of algebraic graph theory, this fast-growing field is concerned with the study of highly symmetric graphs, particularly vertex-transitive graphs, and other combinatorial structures, primarily by group-theoretic techniques. In practice the street goes both ways and these investigations shed new light on permutation groups and related algebraic structures. The book assumes a first course in graph theory and group theory but no specialized knowledge of the theory of permutation groups or vertex-transitive graphs. It begins with the basic material before introducing the field's major problems and most active research themes in order to motivate the detailed discussion of individual topics that follows. Featuring many examples and over 450 exercises, it is an essential introduction to the field for graduate students and a valuable addition to any algebraic graph theorist's bookshelf.

$p$-Adic Analysis, Arithmetic and Singularities (Paperback): Carlos Galindo, Alejandro Melle-Hernandez, Julio Jose... $p$-Adic Analysis, Arithmetic and Singularities (Paperback)
Carlos Galindo, Alejandro Melle-Hernandez, Julio Jose Moyano-Fernandez, Wilson A. Zuniga-Galindo
R3,574 R3,032 Discovery Miles 30 320 Save R542 (15%) Ships in 10 - 15 working days

This volume contains the proceedings of the 2019 Lluis A. Santalo Summer School on $p$-Adic Analysis, Arithmetic and Singularities, which was held from June 24-28, 2019, at the Universidad Internacional Menendez Pelayo, Santander, Spain. The main purpose of the book is to present and analyze different incarnations of the local zeta functions and their multiple connections in mathematics and theoretical physics. Local zeta functions are ubiquitous objects in mathematics and theoretical physics. At the mathematical level, local zeta functions contain geometry and arithmetic information about the set of zeros defined by a finite number of polynomials. In terms of applications in theoretical physics, these functions play a central role in the regularization of Feynman amplitudes and Koba-Nielsen-type string amplitudes, among other applications. This volume provides a gentle introduction to a very active area of research that lies at the intersection of number theory, $p$-adic analysis, algebraic geometry, singularity theory, and theoretical physics. Specifically, the book introduces $p$-adic analysis, the theory of zeta functions, Archimedean, $p$-adic, motivic, singularities of plane curves and their Poincare series, among other similar topics. It also contains original contributions in the aforementioned areas written by renowned specialists. This book is an important reference for students and experts who want to delve quickly into the area of local zeta functions and their many connections in mathematics and theoretical physics. This book is published in cooperation with Real Sociedad Matematica Espanola.

Point-Counting and the Zilber-Pink Conjecture (Hardcover): Jonathan Pila Point-Counting and the Zilber-Pink Conjecture (Hardcover)
Jonathan Pila
R2,794 Discovery Miles 27 940 Ships in 10 - 15 working days

Point-counting results for sets in real Euclidean space have found remarkable applications to diophantine geometry, enabling significant progress on the Andre-Oort and Zilber-Pink conjectures. The results combine ideas close to transcendence theory with the strong tameness properties of sets that are definable in an o-minimal structure, and thus the material treated connects ideas in model theory, transcendence theory, and arithmetic. This book describes the counting results and their applications along with their model-theoretic and transcendence connections. Core results are presented in detail to demonstrate the flexibility of the method, while wider developments are described in order to illustrate the breadth of the diophantine conjectures and to highlight key arithmetical ingredients. The underlying ideas are elementary and most of the book can be read with only a basic familiarity with number theory and complex algebraic geometry. It serves as an introduction for postgraduate students and researchers to the main ideas, results, problems, and themes of current research in this area.

Algebraic Threefolds - With Special Regard to Problems of Rationality (Paperback): Leonard Roth Algebraic Threefolds - With Special Regard to Problems of Rationality (Paperback)
Leonard Roth
R1,369 Discovery Miles 13 690 Ships in 18 - 22 working days
On Finite GK-Dimensional Nichols Algebras over Abelian Groups (Paperback): Nicolas Andruskiewitsch, Ivan Angiono, Istvan... On Finite GK-Dimensional Nichols Algebras over Abelian Groups (Paperback)
Nicolas Andruskiewitsch, Ivan Angiono, Istvan Heckenberger
R2,455 R2,092 Discovery Miles 20 920 Save R363 (15%) Ships in 10 - 15 working days
Cell Complexes, Poset Topology and the Representation Theory of Algebras Arising in Algebraic Combinatorics and Discrete... Cell Complexes, Poset Topology and the Representation Theory of Algebras Arising in Algebraic Combinatorics and Discrete Geometry (Paperback)
Stuart Margolis, Franco Saliola, Benjamin Steinberg
R2,455 R2,092 Discovery Miles 20 920 Save R363 (15%) Ships in 10 - 15 working days
Introduction to Algebraic Geometry (Paperback, 1st ed. 2021): Igor Kriz, Sophie Kriz Introduction to Algebraic Geometry (Paperback, 1st ed. 2021)
Igor Kriz, Sophie Kriz
R1,351 Discovery Miles 13 510 Ships in 9 - 17 working days

The goal of this book is to provide an introduction to algebraic geometry accessible to students. Starting from solutions of polynomial equations, modern tools of the subject soon appear, motivated by how they improve our understanding of geometrical concepts. In many places, analogies and differences with related mathematical areas are explained. The text approaches foundations of algebraic geometry in a complete and self-contained way, also covering the underlying algebra. The last two chapters include a comprehensive treatment of cohomology and discuss some of its applications in algebraic geometry.

(Co)end Calculus (Paperback): Fosco Loregian (Co)end Calculus (Paperback)
Fosco Loregian
R1,721 Discovery Miles 17 210 Ships in 9 - 17 working days

The language of ends and (co)ends provides a natural and general way of expressing many phenomena in category theory, in the abstract and in applications. Yet although category-theoretic methods are now widely used by mathematicians, since (co)ends lie just beyond a first course in category theory, they are typically only used by category theorists, for whom they are something of a secret weapon. This book is the first systematic treatment of the theory of (co)ends. Aimed at a wide audience, it presents the (co)end calculus as a powerful tool to clarify and simplify definitions and results in category theory and export them for use in diverse areas of mathematics and computer science. It is organised as an easy-to-cite reference manual, and will be of interest to category theorists and users of category theory alike.

Berkeley Lectures on p-adic Geometry - (AMS-207) (Paperback): Peter Scholze, Jared Weinstein Berkeley Lectures on p-adic Geometry - (AMS-207) (Paperback)
Peter Scholze, Jared Weinstein
R1,777 Discovery Miles 17 770 Ships in 10 - 15 working days

Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry. In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p-adic geometry. Building on his discovery of perfectoid spaces, Scholze introduced the concept of "diamonds," which are to perfectoid spaces what algebraic spaces are to schemes. The introduction of diamonds, along with the development of a mixed-characteristic shtuka, set the stage for a critical advance in the discipline. In this book, Peter Scholze and Jared Weinstein show that the moduli space of mixed-characteristic shtukas is a diamond, raising the possibility of using the cohomology of such spaces to attack the Langlands conjectures for a reductive group over a p-adic field. This book follows the informal style of the original Berkeley lectures, with one chapter per lecture. It explores p-adic and perfectoid spaces before laying out the newer theory of shtukas and their moduli spaces. Points of contact with other threads of the subject, including p-divisible groups, p-adic Hodge theory, and Rapoport-Zink spaces, are thoroughly explained. Berkeley Lectures on p-adic Geometry will be a useful resource for students and scholars working in arithmetic geometry and number theory.

Dualizable Tensor Categories (Paperback): Christopher L. Douglas, Christopher Schommer-Pries, Noah Snyder Dualizable Tensor Categories (Paperback)
Christopher L. Douglas, Christopher Schommer-Pries, Noah Snyder
R2,165 Discovery Miles 21 650 Ships in 10 - 15 working days
Geometrie Algebrique Reelle (French, Hardcover, 1987 ed.): Jacek Bochnak, et al Geometrie Algebrique Reelle (French, Hardcover, 1987 ed.)
Jacek Bochnak, et al
R2,702 Discovery Miles 27 020 Ships in 18 - 22 working days
Applied Linear Algebra - The Decoupling Principle, Second Edition (Paperback): Lorenzo Sadun Applied Linear Algebra - The Decoupling Principle, Second Edition (Paperback)
Lorenzo Sadun
R2,023 R1,745 Discovery Miles 17 450 Save R278 (14%) Ships in 10 - 15 working days

Linear algebra permeates mathematics, as well as physics and engineering. In this text for junior and senior undergraduates, Sadun treats diagonalization as a central tool in solving complicated problems in these subjects by reducing coupled linear evolution problems to a sequence of simpler decoupled problems. This is the Decoupling Principle. Traditionally, difference equations, Markov chains, coupled oscillators, Fourier series, the wave equation, the Schrodinger equation, and Fourier transforms are treated separately, often in different courses. Here, they are treated as particular instances of the decoupling principle, and their solutions are remarkably similar. By understanding this general principle and the many applications given in the book, students will be able to recognize it and to apply it in many other settings. Sadun includes some topics relating to infinite-dimensional spaces. He does not present a general theory, but enough so as to apply the decoupling principle to the wave equation, leading to Fourier series and the Fourier transform. The second edition contains a series of Explorations. Most are numerical labs in which the reader is asked to use standard computer software to look deeper into the subject. Some explorations are theoretical, for instance, relating linear algebra to quantum mechanics. There is also an appendix reviewing basic matrix operations and another with solutions to a third of the exercises.

Aspects of Mathematics: Rational Points (Paperback, 1984): Gerd Faltings, Gibert Wustholz Aspects of Mathematics: Rational Points (Paperback, 1984)
Gerd Faltings, Gibert Wustholz
R1,746 Discovery Miles 17 460 Ships in 18 - 22 working days
Geometry of Subanalytic and Semialgebraic Sets (Hardcover): Masahiro Shiota Geometry of Subanalytic and Semialgebraic Sets (Hardcover)
Masahiro Shiota
R2,461 Discovery Miles 24 610 Ships in 10 - 15 working days

Subanalytic and semialgebraic sets were introduced for topological and systematic investigations of real analytic and algebraic sets. One of the author's purposes is to show that almost all (known and unknown) properties of subanalytic and semialgebraic sets follow abstractly from some fundamental axioms. Another is to develop methods of proof that use finite processes instead of integration of vector fields. The proofs are elementary, but the results obtained are new and significant - for example, for singularity theorists and topologists. Further, the new methods and tools developed provide solid foundations for further research by model theorists (logicians) who are interested in applications of model theory to geometry. A knowledge of basic topology is required.

Combinatorics, Graph Theory and Computing - SEICCGTC 2020, Boca Raton, USA, March 9-13 (Hardcover, 1st ed. 2022): Frederick... Combinatorics, Graph Theory and Computing - SEICCGTC 2020, Boca Raton, USA, March 9-13 (Hardcover, 1st ed. 2022)
Frederick Hoffman
R3,536 Discovery Miles 35 360 Ships in 10 - 15 working days

This proceedings volume gathers selected, revised papers presented at the 51st Southeastern International Conference on Combinatorics, Graph Theory and Computing (SEICCGTC 2020), held at Florida Atlantic University in Boca Raton, USA, on March 9-13, 2020. The SEICCGTC is broadly considered to be a trendsetter for other conferences around the world - many of the ideas and themes first discussed at it have subsequently been explored at other conferences and symposia. The conference has been held annually since 1970, in Baton Rouge, Louisiana and Boca Raton, Florida. Over the years, it has grown to become the major annual conference in its fields, and plays a major role in disseminating results and in fostering collaborative work. This volume is intended for the community of pure and applied mathematicians, in academia, industry and government, working in combinatorics and graph theory, as well as related areas of computer science and the interactions among these fields.

Higher Categories and Homotopical Algebra (Hardcover): Denis-Charles Cisinski Higher Categories and Homotopical Algebra (Hardcover)
Denis-Charles Cisinski
R1,864 Discovery Miles 18 640 Ships in 10 - 15 working days

This book provides an introduction to modern homotopy theory through the lens of higher categories after Joyal and Lurie, giving access to methods used at the forefront of research in algebraic topology and algebraic geometry in the twenty-first century. The text starts from scratch - revisiting results from classical homotopy theory such as Serre's long exact sequence, Quillen's theorems A and B, Grothendieck's smooth/proper base change formulas, and the construction of the Kan-Quillen model structure on simplicial sets - and develops an alternative to a significant part of Lurie's definitive reference Higher Topos Theory, with new constructions and proofs, in particular, the Yoneda Lemma and Kan extensions. The strong emphasis on homotopical algebra provides clear insights into classical constructions such as calculus of fractions, homotopy limits and derived functors. For graduate students and researchers from neighbouring fields, this book is a user-friendly guide to advanced tools that the theory provides for application.

Berkeley Lectures on p-adic Geometry - (AMS-207) (Hardcover): Peter Scholze, Jared Weinstein Berkeley Lectures on p-adic Geometry - (AMS-207) (Hardcover)
Peter Scholze, Jared Weinstein
R3,774 Discovery Miles 37 740 Ships in 10 - 15 working days

Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry. In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p-adic geometry. Building on his discovery of perfectoid spaces, Scholze introduced the concept of "diamonds," which are to perfectoid spaces what algebraic spaces are to schemes. The introduction of diamonds, along with the development of a mixed-characteristic shtuka, set the stage for a critical advance in the discipline. In this book, Peter Scholze and Jared Weinstein show that the moduli space of mixed-characteristic shtukas is a diamond, raising the possibility of using the cohomology of such spaces to attack the Langlands conjectures for a reductive group over a p-adic field. This book follows the informal style of the original Berkeley lectures, with one chapter per lecture. It explores p-adic and perfectoid spaces before laying out the newer theory of shtukas and their moduli spaces. Points of contact with other threads of the subject, including p-divisible groups, p-adic Hodge theory, and Rapoport-Zink spaces, are thoroughly explained. Berkeley Lectures on p-adic Geometry will be a useful resource for students and scholars working in arithmetic geometry and number theory.

Representations modulaires des groupes reductifs p-adiques. Representations cuspidales de GL(n) (French, Hardcover, 1996 ed.):... Representations modulaires des groupes reductifs p-adiques. Representations cuspidales de GL(n) (French, Hardcover, 1996 ed.)
Marie-France Vigneras
R1,543 Discovery Miles 15 430 Ships in 18 - 22 working days

Taking up the works of Harish-Chandra, Langlands, Borel, Casselman, Bernstein and Zelevinsky, among others, on the complex representation theory of a p -adic reductive group G, the author explores the representations of G over an algebraic closure Fl of a finite field Fl with l1 p elements, which are called 'modular representations'. The main feature of the book is to develop the theory of types over Fl, and to use this theory to prove fundamental results in the theory of modular representations.

"The present book is of evident importance to everyone interested in the representation theory of p-adic groups....The monograph starts on an elementary level laying proper foundations for the things to come and then proceeds directly to results of recent research."

--Zentralblatt

The Classification of the Finite Simple Groups, Number 8 - Part III, Chapters 12-17: The Generic Case, Completed (Hardcover):... The Classification of the Finite Simple Groups, Number 8 - Part III, Chapters 12-17: The Generic Case, Completed (Hardcover)
Daniel Gorenstein, Richard Lyons, Ronald Solomon
R3,262 Discovery Miles 32 620 Ships in 10 - 15 working days

This book completes a trilogy (Numbers 5, 7, and 8) of the series The Classification of the Finite Simple Groups treating the generic case of the classification of the finite simple groups. In conjunction with Numbers 4 and 6, it allows us to reach a major milestone in our series--the completion of the proof of the following theorem: Theorem O: Let G be a finite simple group of odd type, all of whose proper simple sections are known simple groups. Then either G is an alternating group or G is a finite group of Lie type defined over a field of odd order or G is one of six sporadic simple groups. Put another way, Theorem O asserts that any minimal counterexample to the classification of the finite simple groups must be of even type. The work of Aschbacher and Smith shows that a minimal counterexample is not of quasithin even type, while this volume shows that a minimal counterexample cannot be of generic even type, modulo the treatment of certain intermediate configurations of even type which will be ruled out in the next volume of our series.

Lectures on Matrix Field Theory (Paperback, 1st ed. 2017): Badis Ydri Lectures on Matrix Field Theory (Paperback, 1st ed. 2017)
Badis Ydri
R1,375 R1,291 Discovery Miles 12 910 Save R84 (6%) Ships in 9 - 17 working days

These lecture notes provide a systematic introduction to matrix models of quantum field theories with non-commutative and fuzzy geometries. The book initially focuses on the matrix formulation of non-commutative and fuzzy spaces, followed by a description of the non-perturbative treatment of the corresponding field theories. As an example, the phase structure of non-commutative phi-four theory is treated in great detail, with a separate chapter on the multitrace approach. The last chapter offers a general introduction to non-commutative gauge theories, while two appendices round out the text. Primarily written as a self-study guide for postgraduate students - with the aim of pedagogically introducing them to key analytical and numerical tools, as well as useful physical models in applications - these lecture notes will also benefit experienced researchers by providing a reference guide to the fundamentals of non-commutative field theory with an emphasis on matrix models and fuzzy geometries.

Geometry and Physics: Volume I - A Festschrift in honour of Nigel Hitchin (Hardcover): Jorgen Ellegaard Andersen, Andrew... Geometry and Physics: Volume I - A Festschrift in honour of Nigel Hitchin (Hardcover)
Jorgen Ellegaard Andersen, Andrew Dancer, Oscar Garcia-Prada
R3,597 Discovery Miles 35 970 Ships in 10 - 15 working days

Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997. Geometry and Physics: A Festschrift in honour of Nigel Hitchin contain the proceedings of the conferences held in September 2016 in Aarhus, Oxford, and Madrid to mark Nigel Hitchin's 70th birthday, and to honour his far-reaching contributions to geometry and mathematical physics. These texts contain 29 articles by contributors to the conference and other distinguished mathematicians working in related areas, including three Fields Medallists. The articles cover a broad range of topics in differential, algebraic and symplectic geometry, and also in mathematical physics. These volumes will be of interest to researchers and graduate students in geometry and mathematical physics.

The Brauer-Grothendieck Group (Hardcover, 1st ed. 2021): Jean-Louis Colliot-Thelene, Alexei N. Skorobogatov The Brauer-Grothendieck Group (Hardcover, 1st ed. 2021)
Jean-Louis Colliot-Thelene, Alexei N. Skorobogatov
R3,026 Discovery Miles 30 260 Ships in 10 - 15 working days

This monograph provides a systematic treatment of the Brauer group of schemes, from the foundational work of Grothendieck to recent applications in arithmetic and algebraic geometry. The importance of the cohomological Brauer group for applications to Diophantine equations and algebraic geometry was discovered soon after this group was introduced by Grothendieck. The Brauer-Manin obstruction plays a crucial role in the study of rational points on varieties over global fields. The birational invariance of the Brauer group was recently used in a novel way to establish the irrationality of many new classes of algebraic varieties. The book covers the vast theory underpinning these and other applications. Intended as an introduction to cohomological methods in algebraic geometry, most of the book is accessible to readers with a knowledge of algebra, algebraic geometry and algebraic number theory at graduate level. Much of the more advanced material is not readily available in book form elsewhere; notably, de Jong's proof of Gabber's theorem, the specialisation method and applications of the Brauer group to rationality questions, an in-depth study of the Brauer-Manin obstruction, and proof of the finiteness theorem for the Brauer group of abelian varieties and K3 surfaces over finitely generated fields. The book surveys recent work but also gives detailed proofs of basic theorems, maintaining a balance between general theory and concrete examples. Over half a century after Grothendieck's foundational seminars on the topic, The Brauer-Grothendieck Group is a treatise that fills a longstanding gap in the literature, providing researchers, including research students, with a valuable reference on a central object of algebraic and arithmetic geometry.

The Invariant Theory of Matrices (Paperback): Corrado de Concini, Claudio Procesi The Invariant Theory of Matrices (Paperback)
Corrado de Concini, Claudio Procesi
R1,727 Discovery Miles 17 270 Ships in 10 - 15 working days

This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of $m\times m$ matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving the first fundamental theorem that describes a set of generators in the ring of invariants, and the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case requires the development of a collection of tools. These tools and their application to the study of invariants are exlained in an elementary, self-contained way in the book.

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