Homology Of Analytic Sheaves And Duality Theorems

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Homology of Analytic Sheaves and Duality Theorems

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Author : V.D. Golovin
Publisher : Springer
ISBN 13 :
Total Pages : 232 pages
Book Rating : 4.:/5 (5 download)

Book Synopsis Homology of Analytic Sheaves and Duality Theorems by : V.D. Golovin

Download or read book Homology of Analytic Sheaves and Duality Theorems written by V.D. Golovin and published by Springer. This book was released on 1989-04-30 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Translation (from the Russian) of a monograph in which the author provides experts in homological algebra and the theory of topological vector spaces with a systematic and detailed account of results developed largely by himself, during the 1970s. Five chapters, detailed notes and bibliography, the

Homology of Analytic Sheaves and Duality Theorems

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Author : Viktor Dmitrievich Golovin
Publisher :
ISBN 13 : 9785855010879
Total Pages : 210 pages
Book Rating : 4.0/5 (18 download)

Book Synopsis Homology of Analytic Sheaves and Duality Theorems by : Viktor Dmitrievich Golovin

Download or read book Homology of Analytic Sheaves and Duality Theorems written by Viktor Dmitrievich Golovin and published by . This book was released on 1996 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Homology of Analytic Sheaves and Duality Theorems

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Author : V.D. Golovin
Publisher : Springer
ISBN 13 : 9781468416770
Total Pages : 0 pages
Book Rating : 4.4/5 (167 download)

Book Synopsis Homology of Analytic Sheaves and Duality Theorems by : V.D. Golovin

Download or read book Homology of Analytic Sheaves and Duality Theorems written by V.D. Golovin and published by Springer. This book was released on 2013-05-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Spectral Decompositions and Analytic Sheaves

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Author : Jörg Eschmeier
Publisher : Oxford University Press
ISBN 13 : 9780198536673
Total Pages : 378 pages
Book Rating : 4.5/5 (366 download)

Book Synopsis Spectral Decompositions and Analytic Sheaves by : Jörg Eschmeier

Download or read book Spectral Decompositions and Analytic Sheaves written by Jörg Eschmeier and published by Oxford University Press. This book was released on 1996 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rapid developments in multivariable spectral theory have led to important and fascinating results which also have applications in other mathematical disciplines. In this book, various concepts from function theory and complex analytic geometry are drawn together to give a new approach to concrete spectral computations and give insights into new developments in the spectral theory of linear operators. Classical results from cohomology theory of Banach algebras, multidimensional spectral theory, and complex analytic geometry have been freshly interpreted using the language of homological algebra. The advantages of this approach are illustrated by a variety of examples, unexpected applications, and conceptually new ideas that should stimulate further research among mathematicians.

Intersection Homology & Perverse Sheaves

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Author : Laurenţiu G. Maxim
Publisher : Springer Nature
ISBN 13 : 3030276449
Total Pages : 270 pages
Book Rating : 4.0/5 (32 download)

Book Synopsis Intersection Homology & Perverse Sheaves by : Laurenţiu G. Maxim

Download or read book Intersection Homology & Perverse Sheaves written by Laurenţiu G. Maxim and published by Springer Nature. This book was released on 2019-11-30 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout. By giving a taste of the main ideas in the field, the author welcomes new readers to this exciting area at the crossroads of topology, algebraic geometry, analysis, and differential equations. Those looking to delve further into the abstract theory will find ample references to facilitate navigation of both classic and recent literature. Beginning with an introduction to intersection homology from a geometric and topological viewpoint, the text goes on to develop the sheaf-theoretical perspective. Then algebraic geometry comes to the fore: a brief discussion of constructibility opens onto an in-depth exploration of perverse sheaves. Highlights from the following chapters include a detailed account of the proof of the Beilinson–Bernstein–Deligne–Gabber (BBDG) decomposition theorem, applications of perverse sheaves to hypersurface singularities, and a discussion of Hodge-theoretic aspects of intersection homology via Saito’s deep theory of mixed Hodge modules. An epilogue offers a succinct summary of the literature surrounding some recent applications. Intersection Homology & Perverse Sheaves is suitable for graduate students with a basic background in topology and algebraic geometry. By building context and familiarity with examples, the text offers an ideal starting point for those entering the field. This classroom-tested approach opens the door to further study and to current research.

Residues and Duality for Projective Algebraic Varieties

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Author : Ernst Kunz
Publisher : American Mathematical Soc.
ISBN 13 : 0821847600
Total Pages : 177 pages
Book Rating : 4.8/5 (218 download)

Book Synopsis Residues and Duality for Projective Algebraic Varieties by : Ernst Kunz

Download or read book Residues and Duality for Projective Algebraic Varieties written by Ernst Kunz and published by American Mathematical Soc.. This book was released on 2008 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book, which grew out of lectures by E. Kunz for students with a background in algebra and algebraic geometry, develops local and global duality theory in the special case of (possibly singular) algebraic varieties over algebraically closed base fields. It describes duality and residue theorems in terms of Kahler differential forms and their residues. The properties of residues are introduced via local cohomology. Special emphasis is given to the relation between residues to classical results of algebraic geometry and their generalizations." "The contribution by A. Dickenstein gives applications of residues and duality to polynomial solutions of constant coefficient partial differential equations and to problems in interpolation and ideal membership, D. A. Cox explains toric residues and relates them to the earlier text." "The book is intended as an introduction to more advanced treatments and further applications of the subject, to which numerous bibliographical hints are given."--BOOK JACKET.

Arithmetic Duality Theorems

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Author : J. S. Milne
Publisher :
ISBN 13 :
Total Pages : 440 pages
Book Rating : 4.3/5 (97 download)

Book Synopsis Arithmetic Duality Theorems by : J. S. Milne

Download or read book Arithmetic Duality Theorems written by J. S. Milne and published by . This book was released on 1986 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here, published for the first time, are the complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry. The text covers these theorems in Galois cohomology, ,tale cohomology, and flat cohomology and addresses applications in the above areas. The writing is expository and the book will serve as an invaluable reference text as well as an excellent introduction to the subject.

Topology of Singular Spaces and Constructible Sheaves

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Author : Jörg Schürmann
Publisher : Birkhäuser
ISBN 13 : 3034880618
Total Pages : 461 pages
Book Rating : 4.0/5 (348 download)

Book Synopsis Topology of Singular Spaces and Constructible Sheaves by : Jörg Schürmann

Download or read book Topology of Singular Spaces and Constructible Sheaves written by Jörg Schürmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Cohomology of Sheaves

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Author : Birger Iversen
Publisher : Springer Science & Business Media
ISBN 13 : 3642827837
Total Pages : 476 pages
Book Rating : 4.6/5 (428 download)

Book Synopsis Cohomology of Sheaves by : Birger Iversen

Download or read book Cohomology of Sheaves written by Birger Iversen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Methods of Homological Algebra

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Author : Sergei I. Gelfand
Publisher : Springer Science & Business Media
ISBN 13 : 3662032201
Total Pages : 388 pages
Book Rating : 4.6/5 (62 download)

Book Synopsis Methods of Homological Algebra by : Sergei I. Gelfand

Download or read book Methods of Homological Algebra written by Sergei I. Gelfand and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homological algebra first arose as a language for describing topological prospects of geometrical objects. As with every successful language it quickly expanded its coverage and semantics, and its contemporary applications are many and diverse. This modern approach to homological algebra, by two leading writers in the field, is based on the systematic use of the language and ideas of derived categories and derived functors. Relations with standard cohomology theory (sheaf cohomology, spectral sequences, etc.) are described. In most cases complete proofs are given. Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to learn about a modern approach to homological algebra and to use it in their work.

Sheaves on Manifolds

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Author : Masaki Kashiwara
Publisher : Springer Science & Business Media
ISBN 13 : 3662026619
Total Pages : 522 pages
Book Rating : 4.6/5 (62 download)

Book Synopsis Sheaves on Manifolds by : Masaki Kashiwara

Download or read book Sheaves on Manifolds written by Masaki Kashiwara and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Homological Algebra

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Author : S.I. Gelfand
Publisher : Springer Science & Business Media
ISBN 13 : 9783540533733
Total Pages : 240 pages
Book Rating : 4.5/5 (337 download)

Book Synopsis Homological Algebra by : S.I. Gelfand

Download or read book Homological Algebra written by S.I. Gelfand and published by Springer Science & Business Media. This book was released on 1994-03-29 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors. The book contains applications of homological algebra to the theory of sheaves on topological spaces, to Hodge theory, and to the theory of modules over rings of algebraic differential operators (algebraic D-modules). The authors Gelfand and Manin explain all the main ideas of the theory of derived categories. Both authors are well-known researchers and the second, Manin, is famous for his work in algebraic geometry and mathematical physics. The book is an excellent reference for graduate students and researchers in mathematics and also for physicists who use methods from algebraic geometry and algebraic topology.

The Bochner-Martinelli Integral and Its Applications

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Author : Alexander M. Kytmanov
Publisher : Birkhäuser
ISBN 13 : 303489094X
Total Pages : 318 pages
Book Rating : 4.0/5 (348 download)

Book Synopsis The Bochner-Martinelli Integral and Its Applications by : Alexander M. Kytmanov

Download or read book The Bochner-Martinelli Integral and Its Applications written by Alexander M. Kytmanov and published by Birkhäuser. This book was released on 2012-12-06 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Bochner-Martinelli integral representation for holomorphic functions or'sev eral complex variables (which has already become classical) appeared in the works of Martinelli and Bochner at the beginning of the 1940's. It was the first essen tially multidimensional representation in which the integration takes place over the whole boundary of the domain. This integral representation has a universal 1 kernel (not depending on the form of the domain), like the Cauchy kernel in e . However, in en when n > 1, the Bochner-Martinelli kernel is harmonic, but not holomorphic. For a long time, this circumstance prevented the wide application of the Bochner-Martinelli integral in multidimensional complex analysis. Martinelli and Bochner used their representation to prove the theorem of Hartogs (Osgood Brown) on removability of compact singularities of holomorphic functions in en when n > 1. In the 1950's and 1960's, only isolated works appeared that studied the boundary behavior of Bochner-Martinelli (type) integrals by analogy with Cauchy (type) integrals. This study was based on the Bochner-Martinelli integral being the sum of a double-layer potential and the tangential derivative of a single-layer potential. Therefore the Bochner-Martinelli integral has a jump that agrees with the integrand, but it behaves like the Cauchy integral under approach to the boundary, that is, somewhat worse than the double-layer potential. Thus, the Bochner-Martinelli integral combines properties of the Cauchy integral and the double-layer potential.

Sheaf Theory

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Author : Source Wikipedia
Publisher : University-Press.org
ISBN 13 : 9781230585307
Total Pages : 86 pages
Book Rating : 4.5/5 (853 download)

Book Synopsis Sheaf Theory by : Source Wikipedia

Download or read book Sheaf Theory written by Source Wikipedia and published by University-Press.org. This book was released on 2013-09 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 44. Chapters: Abstract differential geometry, Algebraic analysis, Base change, Borel-Moore homology, Coherent duality, Coherent sheaf, Constant sheaf, Cousin problems, D-module, Deligne cohomology, De Rham-Weil theorem, Direct image functor, Direct image with compact support, Exceptional inverse image functor, Exponential sheaf sequence, Flat topology, Gerbe, Germ (mathematics), Godement resolution, Grothendieck topology, Holomorphic sheaf, Hyperfunction, Ideal sheaf, Image functors for sheaves, Injective sheaf, Invertible sheaf, Kripke semantics, Leray's theorem, Leray cover, Leray spectral sequence, Locally constant function, Locally free sheaf, Local cohomology, Local system, Presheaf (category theory), Restriction (mathematics), Ringed space, Sheaf (mathematics), Sheaf cohomology, Sheaf extension, Sheaf spanned by global sections, Spencer cohomology, Stalk (sheaf), Topos, Verdier duality.

Algebraic Geometry II

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Author : I.R. Shafarevich
Publisher : Springer Science & Business Media
ISBN 13 : 3642609252
Total Pages : 270 pages
Book Rating : 4.6/5 (426 download)

Book Synopsis Algebraic Geometry II by : I.R. Shafarevich

Download or read book Algebraic Geometry II written by I.R. Shafarevich and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Arithmetic of Algebraic Curves

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Author : Serguei A. Stepanov
Publisher : Springer Science & Business Media
ISBN 13 : 9780306110368
Total Pages : 444 pages
Book Rating : 4.1/5 (13 download)

Book Synopsis Arithmetic of Algebraic Curves by : Serguei A. Stepanov

Download or read book Arithmetic of Algebraic Curves written by Serguei A. Stepanov and published by Springer Science & Business Media. This book was released on 1994-12-31 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Author S.A. Stepanov thoroughly investigates the current state of the theory of Diophantine equations and its related methods. Discussions focus on arithmetic, algebraic-geometric, and logical aspects of the problem. Designed for students as well as researchers, the book includes over 250 excercises accompanied by hints, instructions, and references. Written in a clear manner, this text does not require readers to have special knowledge of modern methods of algebraic geometry.

Encyclopaedia of Mathematics

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Author : M. Hazewinkel
Publisher : Springer
ISBN 13 : 1489937951
Total Pages : 967 pages
Book Rating : 4.4/5 (899 download)

Book Synopsis Encyclopaedia of Mathematics by : M. Hazewinkel

Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-12-01 with total page 967 pages. Available in PDF, EPUB and Kindle. Book excerpt: