Localization And Sheaves

Author : Jara Pascual,Conchi Vidal,A Verschoren
Publisher : CRC Press
Page : 260 pages
File Size : 47,8 Mb
Release : 1995-11-30
Category : Mathematics
ISBN : 0582273722

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Localization and Sheaves by Jara Pascual,Conchi Vidal,A Verschoren Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 45,6 Mb
Release : 1996
Category : Electronic
ISBN : 9995037041

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Localization and Sheaves by Anonim Pdf

Author : Masaki Kashiwara,Pierre Schapira
Publisher : Springer Science & Business Media
Page : 522 pages
File Size : 44,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662026618

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Sheaves on Manifolds by Masaki Kashiwara,Pierre Schapira Pdf

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.

Author : M. P. Fourman,C. J. Mulvey,D. S. Scott
Publisher : Springer
Page : 798 pages
File Size : 52,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540348498

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Applications of Sheaves by M. P. Fourman,C. J. Mulvey,D. S. Scott Pdf

Author : Masaki Kashiwara,Pierre Schapira
Publisher : Springer Science & Business Media
Page : 496 pages
File Size : 40,8 Mb
Release : 2005-12-19
Category : Mathematics
ISBN : 9783540279501

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Categories and Sheaves by Masaki Kashiwara,Pierre Schapira Pdf

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.

Author : Mallios Anastasios,Zafiris Elias
Publisher : World Scientific
Page : 304 pages
File Size : 43,9 Mb
Release : 2015-09-17
Category : Mathematics
ISBN : 9789814719483

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Differential Sheaves And Connections: A Natural Approach To Physical Geometry by Mallios Anastasios,Zafiris Elias Pdf

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.

Author : Jörg Schürmann
Publisher : Birkhäuser
Page : 461 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880619

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Topology of Singular Spaces and Constructible Sheaves by Jörg Schürmann Pdf

This volume is based on the lecture notes of six courses delivered at a Cimpa Summer School in Temuco, Chile, in January 2001. Leading experts contribute with introductory articles covering a broad area in probability and its applications, such as mathematical physics and mathematics of finance. Written at graduate level, the lectures touch the latest advances on each subject, ranging from classical probability theory to modern developments. Thus the book will appeal to students, teachers and researchers working in probability theory or related fields.

Author : Juan A. Navarro González,Juan B. Sancho de Salas
Publisher : Springer
Page : 196 pages
File Size : 41,6 Mb
Release : 2003-12-15
Category : Mathematics
ISBN : 9783540396659

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C^\infinity - Differentiable Spaces by Juan A. Navarro González,Juan B. Sancho de Salas Pdf

The volume develops the foundations of differential geometry so as to include finite-dimensional spaces with singularities and nilpotent functions, at the same level as is standard in the elementary theory of schemes and analytic spaces. The theory of differentiable spaces is developed to the point of providing a handy tool including arbitrary base changes (hence fibred products, intersections and fibres of morphisms), infinitesimal neighbourhoods, sheaves of relative differentials, quotients by actions of compact Lie groups and a theory of sheaves of Fréchet modules paralleling the useful theory of quasi-coherent sheaves on schemes. These notes fit naturally in the theory of C^\infinity-rings and C^\infinity-schemes, as well as in the framework of Spallek’s C^\infinity-standard differentiable spaces, and they require a certain familiarity with commutative algebra, sheaf theory, rings of differentiable functions and Fréchet spaces.

Author : J.L. Bueso,P. Jara,A Verschoren
Publisher : CRC Press
Page : 296 pages
File Size : 45,5 Mb
Release : 1994-10-20
Category : Mathematics
ISBN : 082479589X

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Compatibility, Stability, and Sheaves by J.L. Bueso,P. Jara,A Verschoren Pdf

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.

Author : Pramod N. Achar
Publisher : American Mathematical Soc.
Page : 562 pages
File Size : 49,7 Mb
Release : 2021-09-27
Category : Education
ISBN : 9781470455972

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Perverse Sheaves and Applications to Representation Theory by Pramod N. Achar Pdf

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.

Author : Anastasios Mallios
Publisher : Springer Science & Business Media
Page : 468 pages
File Size : 42,7 Mb
Release : 1998
Category : Mathematics
ISBN : 0792350057

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Geometry of Vector Sheaves by Anastasios Mallios Pdf

This is the second volume of a two-volume monograph which obtains fundamental notions and results of the standard differential geometry of smooth manifolds, without using differential calculus. Here, the sheaf-theoretic character is emphasized. This has theoretical advantages such as greater perspective, clarity and unification, but also practical benefits ranging from elementary particle physics, via gauge theories and theoretical cosmology (differential spaces), to non-linear PDEs (generalized functions). Thus, more general applications, which are no longer smooth in the classical sense, can be coped with. The treatise might also be construed as a new systematic endeavour to confront the ever-increasing notion that the world around us is far from being smooth enough.

Author : A. Verschoren
Publisher : EDITUM
Page : 100 pages
File Size : 55,6 Mb
Release : 1990
Category : Mathematics
ISBN : 8476849346

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Compatibility and Stability by A. Verschoren Pdf

Author : Joseph Bernstein,Valery Lunts
Publisher : Springer
Page : 145 pages
File Size : 55,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540484301

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Equivariant Sheaves and Functors by Joseph Bernstein,Valery Lunts Pdf

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.

Author : Francis Borceux
Publisher : Cambridge University Press
Page : 544 pages
File Size : 42,9 Mb
Release : 1994-12-08
Category : Mathematics
ISBN : 9780521441803

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Handbook of Categorical Algebra: Volume 3, Sheaf Theory by Francis Borceux Pdf

The Handbook of Categorical Algebra is intended to give, in three volumes, a rather detailed account of what, ideally, everybody working in category theory should know, whatever the specific topic of research they have chosen. The book is planned also to serve as a reference book for both specialists in the field and all those using category theory as a tool. Volume 3 begins with the essential aspects of the theory of locales, proceeding to a study in chapter 2 of the sheaves on a locale and on a topological space, in their various equivalent presentations: functors, etale maps or W-sets. Next, this situation is generalized to the case of sheaves on a site and the corresponding notion of Grothendieck topos is introduced. Chapter 4 relates the theory of Grothendieck toposes with that of accessible categories and sketches, by proving the existence of a classifying topos for all coherent theories.

Author : Lenny Taelman
Publisher : Cambridge University Press
Page : 132 pages
File Size : 48,5 Mb
Release : 2016
Category : Mathematics
ISBN : 9781316502594

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Sheaves and Functions Modulo p by Lenny Taelman Pdf

Describes how to use coherent sheaves and cohomology to prove combinatorial and number theoretical identities over finite fields.