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MARC 21

Derived functors and sheaf cohomology
Tag	Description
020	$a9789811207280
082	$a514.23
099	$a515.14 BRU
100	$aBruzzo, Ugo
245	$aDerived functors and sheaf cohomology$hM$cUgo Bruzzo, Beatriz Graña Otero
260	$aSingapore$bWorld Scientific$c2020
300	$axiii, 199 pages$c23 cm.
440	$aContemporary mathematics and its applications : monographs, expositions and lecture notes$vv. 2
520	$a"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 is 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 Čech 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"--Publisher's website
700	$aGraña Otero, Beatriz