Last edited by Kazratilar
Friday, May 8, 2020 | History

10 edition of Cohomology of sheaves found in the catalog.

# Cohomology of sheaves

## by Birger Iversen

• 177 Want to read
• 38 Currently reading

Published by Springer-Verlag in Berlin, New York .
Written in English

Subjects:
• Sheaf theory.,
• Homology theory.

• Edition Notes

Bibliography: p. [461]-464.

Classifications The Physical Object Statement Birger Iversen. Series Universitext LC Classifications QA612.36 .I93 1986 Pagination xi, 464 p. : Number of Pages 464 Open Library OL2711050M ISBN 10 0387163891 LC Control Number 86003789

Manifolds, Sheaves, and Cohomology / This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between loca. Etale cohomology is an important branch in arithmetic geometry. This book covers the main materials in SGA 1, SGA 4, SGA 4 1/2 and SGA 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, Galois cohomology, etale cohomology, derived categories, base change theorems, duality, and l-adic cohomology.

The cohomology of a sheaf S Sh R X on a paracompact space X can b e computed a follows. Choose a soft (or ﬂabby) resolution of S, i.e., a complex of soft sheaves S 0 d S 1Author: Liviu Nicolaescu. 1 The global section functor Let X be a topological space. Denote by ShX the category of sheaves of abelian groups deﬁned on X and by Abgr the category of abelian groups. ShX is an abelian category and has enough injectives since every sheaf F PShX can be mapped F ãÑ ¹ xPX Fx ãÑ ¹ xPX Ix pq where the second map is the direct product of stalkwise injections Fx ãÑIx into injective.

I need a good reference book where I can learn the cohomology of sheaves through the approach of Čech cohomology. The Hartshorne's book, for example, doesn't help me a lot because he choose the "derived functors approach".   Buy Manifolds, Sheaves, and Cohomology (Springer Studium Mathematik - Master) 1st ed. by Wedhorn, Torsten (ISBN: ) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders/5(4).

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### Cohomology of sheaves by Birger Iversen Download PDF EPUB FB2

The fundamental concepts in the study of locally compact spaces is cohomology with compact support and a particular class of sheaves,the so-called soft sheaves. This class plays a double role as the basic vehicle for the internal theory and is the key to applications in : Springer-Verlag Berlin Heidelberg.

The most satis­ factory general class is that of locally compact spaces and it is the study of such spaces which occupies the central part of this text. The fundamental concepts in the study of locally compact spaces is cohomology with compact support and a particular class of sheaves,the so-called soft sheaves.

13 Cohomology of Sheaves discuss in this book, and we try to provide motivations for the introduction of the concepts and tools involved. These sections introduce topics in the same order in which they are presented in the book.

All historical references are taken from Dieudonn e [8]. This is a. The readership for this book will mostly consist of beginner to intermediate graduate students, and it may serve as the basis for a one-semester course on the cohomology of sheaves and its relation to real and complex manifolds.” (Rui Miguel Saramago, zbMATH)Cited by: 4.

The fundamental concepts in the study of locally compact spaces is cohomology with compact support and a particular class of sheaves,the so-called Cohomology of sheaves book sheaves.

This class plays a double role as the basic vehicle for the internal theory and is the key to applications in : Birger Iversen. In mathematics, sheaf cohomology is the application of homological algebra to analyze the global sections of a sheaf on a topological y speaking, sheaf cohomology describes the obstructions to solving a geometric problem globally when it can be solved locally.

The central work for the study of sheaf cohomology is Grothendieck's Tôhoku paper. The general theory of sheaves is very limited and no essential result is obtainable without turn ing to particular classes of topological spaces. The most satis factory general class is that of locally compact spaces and it is the study of such spaces which occupies the central part of this This text exposes the basic features of cohomology of 5/5(1).

The readership for this book will mostly consist of beginner to intermediate graduate students, and it may serve as the basis for a one-semester course on the cohomology of sheaves and its relation to real and complex manifolds.” (Rui Miguel Saramago, zbMATH Author: Torsten Wedhorn.

The readership for this book will mostly consist of beginner to intermediate graduate students, and it may serve as the basis for a one-semester course on the cohomology of sheaves and its relation to real and complex manifolds.” (Rui Miguel Saramago, zbMATH)Brand: Springer Spektrum.

Singular cohomology. Singular cohomology is a powerful invariant in topology, associating a graded-commutative ring to any topological space. Every continuous map f: X → Y determines a homomorphism from the cohomology ring of Y to that of X; this puts strong restrictions on the possible maps from X to more subtle invariants such as homotopy groups, the cohomology ring tends to be.

COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.

The fundamental concepts in the study of locally compact spaces is cohomology with compact support and a particular class of sheaves, the so-called soft sheaves. This class plays a double role as the basic vehicle for the internal theory and is the key to applications in analysis.

Manifolds, Sheaves, and Cohomology. Authors (view affiliations) Torsten Wedhorn This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry.

and complex manifolds, as a model. The author especially emphasizes the difference between. In the present book, Ueno turns to the theory of sheaves and their cohomology.

Loosely speaking, a sheaf is a way of keeping track of local information defined on a topological space, such as the local holomorphic functions on a complex manifold or the local sections of a vector bundle. COHOMOLOGY OF SHEAVES 6 Surjective.

LetFbeanO∗ X-torsor. Considerthepresheafofsets L 1: U7−→(F(U) ×O X(U))/O∗ X (U)where the action of f ∈O∗ X (U) on (s,g) is (fs,f−1g).Then L 1 is a presheaf of O X-modules by setting (s,g) + (s 0,g) = (s,g+ (s0/s)g0) where s0/sis the local sectionfofO∗ X suchthatfs= s0,andh(s,g) = (s,hg) forhalocalsectionofO X.

In fact, comparing sheaf cohomology to de Rham cohomology and singular cohomology provides a proof of de Rham's theorem that the two cohomology theories are isomorphic. A different approach is by Čech cohomology. Čech cohomology was the first cohomology theory developed for sheaves and it is well-suited to concrete calculations.

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.

Modern algebraic geometry is built upon two fundamental notions: schemes and sheaves. The theory of schemes is presented in the first part of this book (Algebraic Geometry 1: From Algebraic Varieties to Schemes, AMS,Translations of Mathematical Monographs, Volume ).

In the present book, the author turns to the theory of sheaves and their cohomology.3/5(1). I personally won't recommend Bredon's book, rather Iversen's "Cohomology of sheaves" (especially if you are interested in the topological aspects/applications of sheaf theory).

There is also Dimca's "Sheaves in topology". However I should say that the epigraph to this (very good) book is "Do not shoot the pianist", and maybe not without a reason.

Of course, a lot of the general stuff about sites, sheaves, etc., is the same either way. $\endgroup$ – Keenan Kidwell Nov 10 '11 at 4 $\begingroup$ Both his course notes and his text book are good, but they are quite different.

In fact, one can regard this functor as $\mathcal{F} \mapsto \hom_{\mathrm{sheaves}}(\ast, \mathcal{F})$ where $\ast$ is the constant sheaf with one element (the terminal object in the category of all -- not necessarily abelian -- sheaves, so sheaf cohomology can be recovered from the full category of sheaves, or the "topos:" it is a fairly.In the present book, Ueno turns to the theory of sheaves and their cohomology.

Loosely speaking, a sheaf is a way of keeping track of local information defined on a topological space, such as the local holomorphic functions on a complex manifold or the local sections of a vector bundle. To study schemes, it is useful to study the sheaves 4/5(1).Coherent sheaves; Cohomology of coherent sheaves ; Computations of some Hodge numbers ; Deformations and Hodge theory ; Analogies and conjectures ; Further details can be found at official website for the book at Springer.

Errata My thanks to Lizhen Qin for the first comment, and Sandor Kovacs for the rest.