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Homology of Analytic Sheaves and Duality Theorems, V.D. Golovin


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Автор: V.D. Golovin
Название:  Homology of Analytic Sheaves and Duality Theorems
ISBN: 9781468416794
Издательство: Springer
Классификация:
ISBN-10: 1468416790
Обложка/Формат: Paperback
Страницы: 218
Вес: 0.30 кг.
Дата издания: 14.03.2012
Серия: Monographs in Contemporary Mathematics
Язык: English
Размер: 229 x 152 x 12
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: The homology of analytic sheaves is a natural apparatus in the theory of duality on complex spaces. The corresponding apparatus in algebraic geometry was developed by Grothendieck in the fifties. In complex ana- lytic geometry the apparatus of homology was missing until recently, and in its stead the hypercohomology of complex sheaves (the hyper-Ext func- tors) and the Aleksandrov-Cech homology with coefficients in co- presheaves were used. The homology of analytic sheaves, sheaves of germs of homology and homology groups of analytic sheaves, were intro- duced and studied in the mid-seventies in a number of papers by the author. The main goal of this book is to give a systematic and detailed account of the homology theory of analytic sheaves and some of its applications to duality theory on complex spaces and to the theory of hyperfunctions. In order to read this book one must be acquainted with the foundations of ho- mological algebra and the theory of topological vector spaces. Only the most elementary concepts and results from the theory of functions of sev- eral complex variables are assumed to be known. The information needed about sheaves and complex spaces is recounted briefly at the beginning of the fIrst chapter. v. D. Golovin v CONTENTS Chapter 1. ANALYTIC SHEA YES .................................... 1 1. Prelirriinary Information .................................... 1 2. Injectivity Test................................................ 16 3. Local Duality . ....... ... ........ ....... ........... ... ... ..... 24 4. Injective and Global Dimension ........................... 36 5. Properties of Fine Sheaves ................................. 46 Chapter 2. HOMOLOGY THEORY ................................ .. 63 1. Sheaves of Germs of Homology. . . . . . . . . . . . . . .. . . . . . . . . 63 . . .


Categories and Sheaves

Автор: Masaki Kashiwara, Pierre Schapira
Название: Categories and Sheaves
ISBN: 3642066208 ISBN-13(EAN): 9783642066207
Издательство: Springer
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Categories and sheaves, which emerged in the middle of the last century as an enrichment for the concepts of sets and functions, appear almost everywhere in mathematics nowadays.

This book covers categories, homological algebra and sheaves in a systematic and exhaustive manner starting from scratch, and continues with full proofs to an exposition of the most recent results in the literature, and sometimes beyond.

The authors present the general theory of categories and functors, emphasising inductive and projective limits, tensor categories, representable functors, ind-objects and localization. Then they study homological algebra including additive, abelian, triangulated categories and also unbounded derived categories using transfinite induction and accessible objects. Finally, sheaf theory as well as twisted sheaves and stacks appear in the framework of Grothendieck topologies.

Cohomology of Sheaves

Автор: Birger Iversen
Название: Cohomology of Sheaves
ISBN: 3540163891 ISBN-13(EAN): 9783540163893
Издательство: Springer
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Цена: 11878.00 р.
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Factorizable Sheaves and Quantum Groups

Автор: Roman Bezrukavnikov; Michael Finkelberg; Vadim Sch
Название: Factorizable Sheaves and Quantum Groups
ISBN: 3540646191 ISBN-13(EAN): 9783540646198
Издательство: Springer
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Цена: 6282.00 р.
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Описание: Devoted to the geometrical construction of the representations of Lusztig's small quantum groups at roots of unity. This book is suitable for specialists in group representations and algebraic geometry.

Exact Categories and Categories of Sheaves

Автор: M. Barr; P. A. Grillet; D. H. van Osdol
Название: Exact Categories and Categories of Sheaves
ISBN: 3540056785 ISBN-13(EAN): 9783540056782
Издательство: Springer
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Цена: 6288.00 р.
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Equivariant Sheaves and Functors

Автор: Joseph Bernstein; Valery Lunts
Название: Equivariant Sheaves and Functors
ISBN: 3540580719 ISBN-13(EAN): 9783540580713
Издательство: Springer
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Цена: 3487.00 р.
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Описание: Introducing the equivariant derived category of sheaves, this monograph also provides applications to the equivariant intersection cohomology. This theory should benefit specialists in representation theory, algebraic geometry or topology.

Topology of Singular Spaces and Constructible Sheaves

Автор: J?rg Sch?rmann
Название: Topology of Singular Spaces and Constructible Sheaves
ISBN: 3034894244 ISBN-13(EAN): 9783034894241
Издательство: Springer
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Цена: 13974.00 р.
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Описание: 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.

Computational Homology

Автор: Kaczynski
Название: Computational Homology
ISBN: 0387408533 ISBN-13(EAN): 9780387408538
Издательство: Springer
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Цена: 13974.00 р.
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Описание: Uses the computer to take a combinatorial computational approach to homological problems. This interdisciplinary book is aimed at researchers and students in mathematics, computer science, nonlinear dynamics, and engineering.

Uniform Central Limit Theorems

Автор: Dudley
Название: Uniform Central Limit Theorems
ISBN: 0521738415 ISBN-13(EAN): 9780521738415
Издательство: Cambridge Academ
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Цена: 7762.00 р.
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Описание: This second edition of a classic work has been considerably expanded and revised, now with complete proofs of all results, including several new theorems not included in the first edition, such as Talagrand`s generic chaining approach to boundedness of Gaussian processes and Gine and Zinn`s characterization of uniform Donsker classes.

Limit Theorems for Stochastic Processes

Автор: Jacod Jean, Shiryaev Albert N.
Название: Limit Theorems for Stochastic Processes
ISBN: 3540439323 ISBN-13(EAN): 9783540439325
Издательство: Springer
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Цена: 18167.00 р.
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Описание: Initially the theory of convergence in law of stochastic processes was developed quite independently from the theory of martingales, semimartingales and stochastic integrals. Apart from a few exceptions essentially concerning diffusion processes, it is only recently that the relation between the two theories has been thoroughly studied. The authors of this Grundlehren volume, two of the international leaders in the field, propose a systematic exposition of convergence in law for stochastic processes, from the point of view of semimartingale theory, with emphasis on results that are useful for mathematical theory and mathematical statistics. This leads them to develop in detail some particularly useful parts of the general theory of stochastic processes, such as martingale problems, and absolute continuity or contiguity results. The book contains an introduction to the theory of martingales and semimartingales, random measures stochastic integrales, Skorokhod topology, etc., as well as a large number of results which have never appeared in book form, and some entirely new results. The second edition contains some additions to the text and references. Some parts are completely rewritten.

Homology, Genes, and Evolutionary Innovation

Автор: Wagner Geunter P., Wagner Gunter P.
Название: Homology, Genes, and Evolutionary Innovation
ISBN: 0691156468 ISBN-13(EAN): 9780691156460
Издательство: Wiley
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Цена: 7920.00 р.
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Описание: Homology - a similar trait shared by different species and derived from common ancestry, such as a seal`s fin and a bird`s wing - is one of the most fundamental yet challenging concepts in evolutionary biology. This book provides a mechanistically based theory of what homology is and how it arises in evolution.

Coherent Analytic Sheaves

Автор: H. Grauert; R. Remmert
Название: Coherent Analytic Sheaves
ISBN: 3642695841 ISBN-13(EAN): 9783642695841
Издательство: Springer
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Описание: . . . Je mehr ich tiber die Principien der Functionentheorie nachdenke - und ich thue dies unablassig -, urn so fester wird meine Uberzeugung, dass diese auf dem Fundamente algebraischer Wahrheiten aufgebaut werden muss (WEIERSTRASS, Glaubensbekenntnis 1875, Math. Werke II, p. 235). 1. Sheaf Theory is a general tool for handling questions which involve local solutions and global patching. "La notion de faisceau s'introduit parce qu'il s'agit de passer de donnees 'locales' a l'etude de proprietes 'globales'" CAR], p. 622. The methods of sheaf theory are algebraic. The notion of a sheaf was first introduced in 1946 by J. LERAY in a short note Eanneau d'homologie d'une representation, C. R. Acad. Sci. 222, 1366-68. Of course sheaves had occurred implicitly much earlier in mathematics. The "Monogene analytische Functionen", which K. WEIERSTRASS glued together from "Func- tionselemente durch analytische Fortsetzung", are simply the connected components of the sheaf of germs of holomorphic functions on a RIEMANN surface*'; and the "ideaux de domaines indetermines", basic in the work of K. OKA since 1948 (cf. OKA], p. 84, 107), are just sheaves of ideals of germs of holomorphic functions. Highly original contributions to mathematics are usually not appreciated at first. Fortunately H. CARTAN immediately realized the great importance of LERAY'S new abstract concept of a sheaf. In the polycopied notes of his Semina ire at the E. N. S.

Gap-Sheaves and Extension of Coherent Analytic Subsheaves

Автор: Yum-Tong Siu; G?nther Trautmann
Название: Gap-Sheaves and Extension of Coherent Analytic Subsheaves
ISBN: 3540052941 ISBN-13(EAN): 9783540052944
Издательство: Springer
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Цена: 3492.00 р.
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