Sheaves
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Categories And Sheaves
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Author : Masaki Kashiwara
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-19
Categories And Sheaves written by Masaki Kashiwara and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-19 with Mathematics categories.
Categories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and sheaves in a systematic manner starting from scratch and continuing with full proofs to the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasizing inductive and projective limits, tensor categories, representable functors, ind-objects and localization.
Categories And Sheaves
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Author : Masaki Kashiwara
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-10-20
Categories And Sheaves written by Masaki Kashiwara and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-20 with Mathematics categories.
Categories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and sheaves in a systematic manner starting from scratch and continuing with full proofs to the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasizing inductive and projective limits, tensor categories, representable functors, ind-objects and localization.
Sheaves In Geometry And Logic
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Author : Saunders MacLane
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Sheaves In Geometry And Logic written by Saunders MacLane and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Sheaves arose in geometry as coefficients for cohomology and as descriptions of the functions appropriate to various kinds of manifolds. Sheaves also appear in logic as carriers for models of set theory. This text presents topos theory as it has developed from the study of sheaves. Beginning with several examples, it explains the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to logic.
Manifolds Sheaves And Cohomology
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Author : Torsten Wedhorn
language : en
Publisher: Springer
Release Date : 2016-07-25
Manifolds Sheaves And Cohomology written by Torsten Wedhorn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-25 with Mathematics categories.
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 local and global questions. Cohomology theory of sheaves is introduced and its usage is illustrated by many examples.
Cohomology Of Sheaves
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Author : Birger Iversen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Cohomology Of Sheaves written by Birger Iversen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This text exposes the basic features of cohomology of sheaves and its applications. 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 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. This class plays a double role as the basic vehicle for the internal theory and is the key to applications in analysis. The basic example of a soft sheaf is the sheaf of smooth functions on ~n or more generally on any smooth manifold. A rather large effort has been made to demon strate the relevance of sheaf theory in even the most elementary analysis. This process has been reversed in order to base the fundamental calculations in sheaf theory on elementary analysis.
Exact Categories And Categories Of Sheaves
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Author : M. Barr
language : en
Publisher: Springer
Release Date : 2006-11-15
Exact Categories And Categories Of Sheaves written by M. Barr and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Sheaves On Manifolds
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Author : Masaki Kashiwara
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Sheaves On Manifolds written by Masaki Kashiwara and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Sheaf Theory is modern, active field of mathematics at the intersection of algebraic topology, algebraic geometry and partial differential equations. This volume offers a comprehensive and self-contained treatment of Sheaf Theory from the basis up, with emphasis on the microlocal point of view. From the reviews: "Clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics." –Bulletin of the L.M.S.
Localization And Sheaves
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Author : Jara Pascual
language : en
Publisher: CRC Press
Release Date : 1995-11-30
Localization And Sheaves written by Jara Pascual and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-11-30 with Mathematics categories.
This book completely solves the problem of representing rings (and modules over them), which are locally noetherian over subsets of their prime spectrum by structure sheaves over this subset. In order to realise this, one has to develop the necessary localization theory as well as to study local equivalents of familiar concepts like the Artin-Rees property, Ore sets and the second layer condition. The first part of the book is introductory and self-contained, and might serve as a starting course (at graduate level) on localization theory within Grothendieck categories. The second part is more specialised and provides the basic machinery needed to effectively these structure sheaves, as well as to study their functorial behaviour. In this way, the book should be viewed as a first introduction to what should be called relative noncommutative algebraic geometry.
Perverse Sheaves And Applications To Representation Theory
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Author : Pramod N. Achar
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-09-27
Perverse Sheaves And Applications To Representation Theory written by Pramod N. Achar and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-27 with Education categories.
Since its inception around 1980, the theory of perverse sheaves has been a vital tool of fundamental importance in geometric representation theory. This book, which aims to make this theory accessible to students and researchers, is divided into two parts. The first six chapters give a comprehensive account of constructible and perverse sheaves on complex algebraic varieties, including such topics as Artin's vanishing theorem, smooth descent, and the nearby cycles functor. This part of the book also has a chapter on the equivariant derived category, and brief surveys of side topics including étale and ℓ-adic sheaves, D-modules, and algebraic stacks. The last four chapters of the book show how to put this machinery to work in the context of selected topics in geometric representation theory: Kazhdan-Lusztig theory; Springer theory; the geometric Satake equivalence; and canonical bases for quantum groups. Recent developments such as the p-canonical basis are also discussed. The book has more than 250 exercises, many of which focus on explicit calculations with concrete examples. It also features a 4-page “Quick Reference” that summarizes the most commonly used facts for computations, similar to a table of integrals in a calculus textbook.
Equivariant Sheaves And Functors
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Author : Joseph Bernstein
language : en
Publisher: Springer
Release Date : 2006-11-15
Equivariant Sheaves And Functors written by Joseph Bernstein and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
The equivariant derived category of sheaves is introduced. All usual functors on sheaves are extended to the equivariant situation. Some applications to the equivariant intersection cohomology are given. The theory may be useful to specialists in representation theory, algebraic geometry or topology.