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Derived functors and sheaf cohomology

Bruzzo, U.

Derived functors and sheaf cohomology

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Derived functors and sheaf cohomologyUgo Bruzzo, Beatriz Graña Otero.
作者:	Bruzzo, U.
其他作者:	Graña Otero, Beatriz.
出版者:	Singapore :World Scientific,c2020.
面頁冊數:	1 online resource (xiii, 199 p.)
標題:	Functor theory.
電子資源:	https://www.worldscientific.com/worldscibooks/10.1142/11473#t=toc
ISBN:	9789811207297$q(ebook)

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: 9789811207297$q(ebook)Subjects--Topical Terms:

206298
Functor theory.

LC Class. No.: QA169 / .B78 2020

Dewey Class. No.: 514/.23

Derived functors and sheaf cohomology
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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.
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