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Showing 1 - 5 of 5 matches in All Departments
This second volume introduces the concept of shemes, reviews some
commutative algebra and introduces projective schemes. The
finiteness theorem for coherent sheaves is proved, here again the
techniques of homological algebra and sheaf cohomology are needed.
In the last two chapters, projective curves over an arbitrary
ground field are discussed, the theory of Jacobians is developed,
and the existence of the Picard scheme is proved.
In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.
This book and the following second volume is an introduction into
modern algebraic geometry. In the first volume the methods of
homological algebra, theory of sheaves, and sheaf cohomology are
developed. These methods are indispensable for modern algebraic
geometry, but they are also fundamental for other branches of
mathematics and of great interest in their own.
This volume contains the Proceedings of the International Workshop "Complex Analysis", which was held from February 12-16, 1990, in Wuppertal (Germany) in honour of H. Grauert, one of the most creative mathematicians in Complex Analysis of this century. In complete accordance with the width of the work of Grauert the book contains research notes and longer articles of many important mathematicians from all areas of Complex Analysis (Altogether there a re 49 articles in the volume). Some of the main subjects are: Cau chy-Riemann Equations with estimates, q-convexity, CR structures, deformation theory, envelopes of holomorphy, function algebras, complex group actions, Hodge theory, instantons, Kahler geometry, Lefschetz theorems, holomorphic mappings, Nevanlinna theory, com plex singularities, twistor theory, uniformization.
Quantum cohomology, the theory of Frobenius manifolds and the
relations to integrable systems are flourishing areas since the
early 90's.
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