Derived Functors And Sheaf Cohomology (Hardcover)

The aim of the book is to present a precise and comprehensive introduction to the basic theory of derived functors, with an emphasis on sheaf cohomology and spectral sequences. It keeps the treatment as simple as possible, aiming at the same time to provide a number of examples, mainly from sheaf theory, and also from algebra.The first part of the book provides the foundational material: Chapter 1 deals with category theory and homological algebra. Chapter 2 is devoted to the development of the theory of derived functors, based on the notion of injective object. In particular, the universal properties of derived functors are stressed, with a view to make the proofs in the following chapters as simple and natural as possible. Chapter 3 provides a rather thorough introduction to sheaves, in a general topological setting. Chapter 4 introduces sheaf cohomology as a derived functor, and, after also defining Cech cohomology, develops a careful comparison between the two cohomologies which is a detailed analysis not easily available in the literature. This comparison is made using general, universal properties of derived functors. This chapter also establishes the relations with the de Rham and Dolbeault cohomologies. Chapter 5 offers a friendly approach to the rather intricate theory of spectral sequences by means of the theory of derived triangles, which is precise and relatively easy to grasp. It also includes several examples of specific spectral sequences. Readers will find exercises throughout the text, with additional exercises included at the end of each chapter.

General

Imprint:	World Scientific Publishing Co Pte Ltd
Country of origin:	Singapore
Series:	Contemporary Mathematics And Its Applications: Monographs, Expositions And Lecture Notes, 2
Release date:	March 2020
First published:	2020
Authors:	Ugo Bruzzo • Beatriz Grana Otero
Dimensions:	160 x 235 x 19mm (L x W x T)
Format:	Hardcover
Pages:	216
ISBN-13:	978-981-12-0728-0
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General
LSN:	981-12-0728-3
Barcode:	9789811207280

Is the information for this product incomplete, wrong or inappropriate? Let us know about it.

Does this product have an incorrect or missing image? Send us a new image.

Is this product missing categories? Add more categories.

Review This Product

No reviews yet - be the first to create one!