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Derived functors and sheaf cohomology

Bruzzo, U.

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Derived functors and sheaf cohomology

Record Type:	Electronic resources : Monograph/item
Title/Author:	Derived functors and sheaf cohomology/ Ugo Bruzzo, Beatriz Graña Otero.
Author:	Bruzzo, U.
other author:	Graña Otero, Beatriz.
Published:	Singapore :World Scientific, : c2020.,
Description:	1 online resource (xiii, 199 p.)
Subject:	Functor theory. -
Online resource:	https://www.worldscientific.com/worldscibooks/10.1142/11473#t=toc
ISBN:	9789811207297

Derived functors and sheaf cohomology
Bruzzo, U.

Derived functors and sheaf cohomology[electronic resource] /Ugo Bruzzo, Beatriz Graña Otero. - 1st ed. - Singapore :World Scientific,c2020. - 1 online resource (xiii, 199 p.) - Contemporary mathematics and its applications : monographs, expositions and lecture notes,v. 22591-7668 ;. - Contemporary mathematics and its applications : monographs, expositions and lecture notes ;v. 2..

Includes bibliographical references and index.

"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.

Mode of access: World Wide Web.

ISBN: 9789811207297Subjects--Topical Terms:

735159
Functor theory.

LC Class. No.: QA169 / .B78 2020

Dewey Class. No.: 514/.23

Derived functors and sheaf cohomology
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020 $a 9789811207297 $q (ebook)
020 $a 9811207291 $q (ebook)
020 $z 9789811207280 $q (hbk.)
020 $z 9811207283 $q (hbk.)
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040 $a WSPC $b eng $c WSPC
050 0 4 $a QA169 $b .B78 2020
082 0 4 $a 514/.23 $2 23
100 1 $a Bruzzo, U. $q (Ugo) $3 860651
245 1 0 $a Derived functors and sheaf cohomology $h [electronic resource] / $c Ugo Bruzzo, Beatriz Graña Otero.
250 $a 1st ed.
260 $a Singapore : $b World Scientific, $c c2020.
300 $a 1 online resource (xiii, 199 p.)
490 1 $a Contemporary mathematics and its applications : monographs, expositions and lecture notes, $x 2591-7668 ; $v v. 2
504 $a Includes bibliographical references and index.
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.
538 $a Mode of access: World Wide Web.
538 $a System requirements: Adobe Acrobat Reader.
588 $a Description based on print version record.
650 0 $a Functor theory. $3 735159
650 0 $a Sheaf theory. $3 612610
650 0 $a Spectral sequences (Mathematics) $3 701647
700 1 $a Graña Otero, Beatriz. $3 3512740
830 0 $a Contemporary mathematics and its applications : monographs, expositions and lecture notes ; $v v. 2. $3 3512741
856 4 0 $u https://www.worldscientific.com/worldscibooks/10.1142/11473#t=toc