Equivariant cohomology in algebraic geometry, Anderson, David (ohio State University) Fulton, William (university Of Michigan, Ann Arbor)
Автор: Tu Loring W. Название: Introductory Lectures on Equivariant Cohomology: (ams-204) ISBN: 0691191743 ISBN-13(EAN): 9780691191744 Издательство: Wiley Рейтинг: Цена: 27971 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology. Equivariant cohomology is concerned with the algebraic topology of spaces with a group action, or in other words, with symmetries of spaces. First defined in the 1950s, it has been introduced into K-theory and algebraic geometry, but it is in algebraic topology that the concepts are the most transparent and the proofs are the simplest. One of the most useful applications of equivariant cohomology is the equivariant localization theorem of Atiyah-Bott and Berline-Vergne, which converts the integral of an equivariant differential form into a finite sum over the fixed point set of the group action, providing a powerful tool for computing integrals over a manifold. Because integrals and symmetries are ubiquitous, equivariant cohomology has found applications in diverse areas of mathematics and physics.
Assuming readers have taken one semester of manifold theory and a year of algebraic topology, Loring Tu begins with the topological construction of equivariant cohomology, then develops the theory for smooth manifolds with the aid of differential forms. To keep the exposition simple, the equivariant localization theorem is proven only for a circle action. An appendix gives a proof of the equivariant de Rham theorem, demonstrating that equivariant cohomology can be computed using equivariant differential forms. Examples and calculations illustrate new concepts. Exercises include hints or solutions, making this book suitable for self-study.
This book studies the interplay between the geometry and topology of locally symmetric spaces, and the arithmetic aspects of the special values of L-functions.
The authors study the cohomology of locally symmetric spaces for GL(N) where the cohomology groups are with coefficients in a local system attached to a finite-dimensional algebraic representation of GL(N). The image of the global cohomology in the cohomology of the Borel-Serre boundary is called Eisenstein cohomology, since at a transcendental level the cohomology classes may be described in terms of Eisenstein series and induced representations. However, because the groups are sheaf-theoretically defined, one can control their rationality and even integrality properties. A celebrated theorem by Langlands describes the constant term of an Eisenstein series in terms of automorphic L-functions. A cohomological interpretation of this theorem in terms of maps in Eisenstein cohomology allows the authors to study the rationality properties of the special values of Rankin-Selberg L-functions for GL(n) x GL(m), where n + m = N. The authors carry through the entire program with an eye toward generalizations.
This book should be of interest to advanced graduate students and researchers interested in number theory, automorphic forms, representation theory, and the cohomology of arithmetic groups.
Автор: Tu Loring W. Название: Introductory Lectures on Equivariant Cohomology: (ams-204) ISBN: 0691191751 ISBN-13(EAN): 9780691191751 Издательство: Wiley Рейтинг: Цена: 12870 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology. Equivariant cohomology is concerned with the algebraic topology of spaces with a group action, or in other words, with symmetries of spaces. First defined in the 1950s, it has been introduced into K-theory and algebraic geometry, but it is in algebraic topology that the concepts are the most transparent and the proofs are the simplest. One of the most useful applications of equivariant cohomology is the equivariant localization theorem of Atiyah-Bott and Berline-Vergne, which converts the integral of an equivariant differential form into a finite sum over the fixed point set of the group action, providing a powerful tool for computing integrals over a manifold. Because integrals and symmetries are ubiquitous, equivariant cohomology has found applications in diverse areas of mathematics and physics.
Assuming readers have taken one semester of manifold theory and a year of algebraic topology, Loring Tu begins with the topological construction of equivariant cohomology, then develops the theory for smooth manifolds with the aid of differential forms. To keep the exposition simple, the equivariant localization theorem is proven only for a circle action. An appendix gives a proof of the equivariant de Rham theorem, demonstrating that equivariant cohomology can be computed using equivariant differential forms. Examples and calculations illustrate new concepts. Exercises include hints or solutions, making this book suitable for self-study.
Автор: Hanno Ulrich Название: Fixed Point Theory of Parametrized Equivariant Maps ISBN: 3540501878 ISBN-13(EAN): 9783540501879 Издательство: Springer Рейтинг: Цена: 3819 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Discusses general properties of G-ENRBs - Euclidean Neighbourhood Retracts over B with action of a compact Lie group G - and their relations with fibrations, continuous submersions, and fibre bundles. This book presents equivariant cohomology theory, showing that equivariant fixed point theory is isomorphic to equivariant stable cohomotopy theory.
Автор: Witherspoon, Sarah J. Название: Hochschild cohomology for algebras ISBN: 1470449315 ISBN-13(EAN): 9781470449315 Издательство: Eurospan Рейтинг: Цена: 15952 р. Наличие на складе: Поставка под заказ.
Описание: This book gives a thorough and self-contained introduction to the theory of Hochschild cohomology for algebras and includes many examples and exercises. The book then explores Hochschild cohomology as a Gerstenhaber algebra in detail, the notions of smoothness and duality, algebraic deformation theory, infinity structures, support varieties, and connections to Hopf algebra cohomology. Useful homological algebra background is provided in an appendix. The book is designed both as an introduction for advanced graduate students and as a resource for mathematicians who use Hochschild cohomology in their work.
Автор: Klas Diederich; G?nter Harder Название: Lectures on Algebraic Geometry I ISBN: 3834819921 ISBN-13(EAN): 9783834819925 Издательство: Springer Рейтинг: Цена: 13315 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Categories, Products, Projective and Inductive Limits - Basic Concepts of Homological Algebra - Sheaves - Cohomology of Sheaves - Compact Riemann surfaces and Abelian Varieties
Автор: I.R. Shafarevich; V.I. Danilov; R. Treger; V.A. Is Название: Algebraic Geometry II ISBN: 3642646077 ISBN-13(EAN): 9783642646072 Издательство: Springer Рейтинг: Цена: 12244 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This two-part volume contains numerous examples and insights on various topics. The authors have taken pains to present the material rigorously and coherently. This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetic algebraic geometry, complex analysis and related fields.
Автор: Ragnar-Olaf Buchweitz Название: Maximal Cohen-Macaulay Modules and Tate Cohomology ISBN: 1470453401 ISBN-13(EAN): 9781470453404 Издательство: Eurospan Рейтинг: Цена: 21050 р. Наличие на складе: Поставка под заказ.
Описание: Presents a lightly edited version of the unpublished manuscript Maximal Cohen-Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz. The central objects of study are maximal Cohen-Macaulay modules over (not necessarily commutative) Gorenstein rings.
For more than thirty years the senior author has been trying to learn algebraic geometry. In the process he discovered that many of the classic textbooks in algebraic geometry require substantial knowledge of cohomology, homological algebra, and sheaf theory. In an attempt to demystify these abstract concepts and facilitate understanding for a new generation of mathematicians, he along with co-author wrote this book for an audience who is familiar with basic concepts of linear and abstract algebra, but who never has had any exposure to the algebraic geometry or homological algebra. As such this book consists of two parts. The first part gives a crash-course on the homological and cohomological aspects of algebraic topology, with a bias in favor of cohomology. The second part is devoted to presheaves, sheaves, Cech cohomology, derived functors, sheaf cohomology, and spectral sequences. All important concepts are intuitively motivated and the associated proofs of the quintessential theorems are presented in detail rarely found in the standard texts.
Автор: Andrй Yves, Baldassarri Francesco, Cailotto Maurizio Название: de Rham Cohomology of Differential Modules on Algebraic Varieties ISBN: 3030397211 ISBN-13(EAN): 9783030397210 Издательство: Springer Цена: 18366 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: "...A nice feature of the book [is] that at various points the authors provide examples, or rather counterexamples, that clearly show what can go wrong...This is a nicely-written book [that] studies algebraic differential modules in several variables."--Mathematical Reviews
Автор: Andrй Yves, Baldassarri Francesco, Cailotto Maurizio Название: de Rham Cohomology of Differential Modules on Algebraic Varieties ISBN: 3030397181 ISBN-13(EAN): 9783030397180 Издательство: Springer Рейтинг: Цена: 18366 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: "...A nice feature of the book [is] that at various points the authors provide examples, or rather counterexamples, that clearly show what can go wrong...This is a nicely-written book [that] studies algebraic differential modules in several variables."--Mathematical Reviews
Автор: Bialynicki-Birula A. Название: Algebraic Quotients. Torus Actions and Cohomology. The Adjoi ISBN: 3642077455 ISBN-13(EAN): 9783642077456 Издательство: Springer Рейтинг: Цена: 21428 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This is the second volume of the new subseries "Invariant Theory and Algebraic Transformation Groups". Bialynicki-Birula is to present the main trends and achievements of research in the theory of quotients by actions of algebraic groups. This theory contains geometric invariant theory with various applications to problems of moduli theory.
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