Localization And Sheaves
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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.
Localization And Sheaves
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Author :
language : en
Publisher:
Release Date : 1996
Localization And Sheaves written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Differential Sheaves And Connections A Natural Approach To Physical Geometry
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Author : Anastasios Mallios
language : en
Publisher: World Scientific
Release Date : 2015-09-17
Differential Sheaves And Connections A Natural Approach To Physical Geometry written by Anastasios Mallios and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-17 with Mathematics categories.
This unique book provides a self-contained conceptual and technical introduction to the theory of differential sheaves. This serves both the newcomer and the experienced researcher in undertaking a background-independent, natural and relational approach to 'physical geometry'. In this manner, this book is situated at the crossroads between the foundations of mathematical analysis with a view toward differential geometry and the foundations of theoretical physics with a view toward quantum mechanics and quantum gravity. The unifying thread is provided by the theory of adjoint functors in category theory and the elucidation of the concepts of sheaf theory and homological algebra in relation to the description and analysis of dynamically constituted physical geometric spectrums.
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.
Applications Of Sheaves
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Author : M. P. Fourman
language : en
Publisher: Springer
Release Date : 2006-11-15
Applications Of Sheaves written by M. P. Fourman 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.
From the reviews: This book is devoted to the study of sheaves by microlocal methods..(it) may serve as a reference source as well as a textbook on this new subject. Houzel's historical overview of the development of sheaf theory will identify important landmarks for students and will be a pleasure to read for specialists. Math. Reviews 92a (1992). The book is clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics.(...)The book can be strongly recommended to a younger mathematician enthusiastic to assimilate a new range of techniques allowing flexible application to a wide variety of problems. Bull. L.M.S. (1992)
Topology Of Singular Spaces And Constructible Sheaves
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Author : Jörg Schürmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-10-24
Topology Of Singular Spaces And Constructible Sheaves written by Jörg Schürmann 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 2003-10-24 with Mathematics categories.
Assuming that the reader is familiar with sheaf theory, the book gives a self-contained introduction to the theory of constructible sheaves related to many kinds of singular spaces, such as cell complexes, triangulated spaces, semialgebraic and subanalytic sets, complex algebraic or analytic sets, stratified spaces, and quotient spaces. The relation to the underlying geometrical ideas are worked out in detail, together with many applications to the topology of such spaces. All chapters have their own detailed introduction, containing the main results and definitions, illustrated in simple terms by a number of examples. The technical details of the proof are postponed to later sections, since these are not needed for the applications.
Compatibility Stability And Sheaves
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Author : J.L. Bueso
language : en
Publisher: CRC Press
Release Date : 1994-10-20
Compatibility Stability And Sheaves written by J.L. Bueso and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-10-20 with Mathematics categories.
Integrates fundamental techniques from algebraic geometry, localization theory and ring theory, and demonstrates how each topic is enhanced by interaction with others, providing new results within a common framework. Technical conclusions are presented and illustrated with concrete examples.
Sheaves And Functions Modulo P
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Author : Lenny Taelman
language : en
Publisher: Cambridge University Press
Release Date : 2016
Sheaves And Functions Modulo P written by Lenny Taelman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Mathematics categories.
Describes how to use coherent sheaves and cohomology to prove combinatorial and number theoretical identities over finite fields.
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.