Etale Cohomology Theory

Author: Lei Fu
Publisher: World Scientific
ISBN: 9814675105
Size: 58.21 MB
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Etale cohomology is an important branch in arithmetic geometry. This book covers the main materials in SGA 1, SGA 4, SGA 4 1/2 and SGA 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, Galois cohomology, etale cohomology, derived categories, base change theorems, duality, and ℓ-adic cohomology. The prerequisites for reading this book are basic algebraic geometry and advanced commutative algebra. Contents:Descent TheoryEtale Morphisms and Smooth MorphismsEtale Fundamental GroupsGroup Cohomology and Galois CohomologyEtale CohomologyDerived Categories and Derived FunctorsBase Change TheoremsDualityFiniteness Theoremsℓ-Adic Cohomology Readership: Graduate students and researchers in pure mathematics. Key Features:This is a revised version of an earlier edition, in which some errors and misprints are corrected, and some paragraphs are rewritten for better exposition. While the most complete treatment on etale cohomology is in SGA 1, 4, 4 1/2 and 5, which is about 3000 pages long, the existing textbooks on etale cohomology theory are, however, incomplete. This book, at about 600 pages, gives a relatively complete treatment of etale cohomology theoryTo achieve an understanding of this book, the reader is only assumed to be familiar with basic algebraic geometry (up to the level of the first three chapters in Algebraic Geometry by R Hartshorne, Springer-Verlag, 1977) and advanced commutative algebra (up to the level of Commutative Algebra by H Matsumura, Benjamin, New York, 1970)Keywords:Etale Topology;Sheaf;Cohomology;Base Change Theorem;Duality;L-Adic CohomologyReview: Reviews of the First Edition: “A very nice feature of Fu's work is the inclusion of some relevant topics, that are covered only briefly (or not at all) in other references. As is the case throughout the book, proofs are given for almost all results in these chapters. One should also remark that precise hypotheses are explicitly stated in most cases for each result. This shall prove very handy when using the book as a reference.” Mathematical Reviews “The book will certainly be very useful to anybody wishing to understand the key tools and results in étale cohomology theory, together with their proofs… Any reader with adequate background and an interest in seriously studying étale cohomology will find the thoroughness of this book really useful.” MathSciNet

A Brief Introduction To Symplectic And Contact Manifolds

Author: Augustin Banyaga
Publisher: World Scientific
ISBN: 9814696722
Size: 35.44 MB
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The book introduces the basic notions in Symplectic and Contact Geometry at the level of the second year graduate student. It also contains many exercises, some of which are solved only in the last chapter. We begin with the linear theory, then give the definition of symplectic manifolds and some basic examples, review advanced calculus, discuss Hamiltonian systems, tour rapidly group and the basics of contact geometry, and solve problems in chapter 8. The material just described can be used as a one semester course on Symplectic and Contact Geometry. The book contains also more advanced material, suitable to advanced graduate students and researchers. Contents: Symplectic Vector SpacesSymplectic ManifoldsHamiltonian Systems and Poisson AlgebraGroup ActionsContact ManifoldsSolutions of Selected ExercisesEpilogue: The C0-Symplectic and Contact Topology Readership: Graduate students, researchers and more advanced mathematicians. Symplectic;Contact GeometryKey Features: It is briefThe easy part has been tested and been used for a short courseThe advanced material develops things related to one of the author's research furtherThere is no book, going from the very elementary part to the very advanced level, like this one

Etale Cohomology Theory

Author: Lei Fu
Publisher: World Scientific
ISBN: 9814307726
Size: 20.94 MB
Format: PDF
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Etale cohomology is an important branch in arithmetic geometry. This book covers the main materials in SGA 1, SGA 4, SGA 4 1/2 and SGA 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, Galois cohomology, etale cohomology, derived categories, base change theorems, duality, and l-adic cohomology. The prerequisites for reading this book are basic algebraic geometry and advanced commutative algebra.

Contemporary Trends In Algebraic Geometry And Algebraic Topology

Author: Shiing-Shen Chern
Publisher: World Scientific
ISBN: 9814488518
Size: 58.54 MB
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The Wei-Liang Chow and Kuo-Tsai Chen Memorial Conference was proposed and held by Prof S S Chern in Nankai Institute of Mathematics. It was devoted to memorializing those two outstanding and original Chinese mathematicians who had made significant contributions to algebraic geometry and algebraic topology, respectively. It also provided a forum for leading mathematicians to expound and discuss their views on new ideas in these fields, as well as trends in 21st Century mathematics. About 100 mathematicians participated in the conference, including Sir Michael Atiyah, Jacob Palis, Phillip Griffiths, David Eisenbud, Philippe Tondeur, Yujiro Kawamata, Tian Gang, etc. This invaluable volume contains the selected papers presented at the conference. The topics include canonical maps of Gorenstein 3-folds, fundamental groups of algebraic curves, Chen's interated integrals, algebraic fiber spaces, and others. Contents:Mathematics in the 20th Century (M Atiyah)The Φ4 of Minimal Gorenstein 3-Folds of General Type (M Chen)Morphisms of Curves and the Fundamental Group (M Cushman)Iterated Integrals and Algebraic Cycles: Examples and Prospects (R Hain)Chen's Interated Integrals and Algebraic Cycles (B Harris)On Algebraic Fiber Spaces (Y Kawamata)Local Holomorphic Isometric Embeddings Arising from Correspondences in the Rank-1 Case (N Mok)Multiple Polylogarithms: Analytic Continuation, Monodromy, and Variations of Mixed Hodge Structures (J Zhao)Deformation Types of Real and Complex Manifolds (F Catanese)Wei-Liang Chow, 1911–1995 (S S Chern)Comments on Chow's Work (S Lang)The Life and Work of Kuo-Tsai Chen (R Hain & Ph Tondeur) Readership: Graduate students and researchers in geometry and topology. Keywords:

Riemann Finsler Geometry

Author: Shiing-Shen Chern
Publisher: World Scientific
ISBN: 9812383573
Size: 78.35 MB
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Riemann-Finsler geometry is a subject that concerns manifolds with Finsler metrics, including Riemannian metrics. It has applications in many fields of the natural sciences. Curvature is the central concept in Riemann-Finsler geometry. This invaluable textbook presents detailed discussions on important curvatures such the Cartan torsion, the S-curvature, the Landsberg curvature and the Riemann curvature. It also deals with Finsler metrics with special curvature or geodesic properties, such as projectively flat Finsler metrics, Berwald metrics, Finsler metrics of scalar curvature or isotropic S-curvature, etc. Instructive examples are given in abundance, for further description of some important geometric concepts. The text includes the most recent results, although many of the problems discussed are classical. Graduate students and researchers in differential geometry.

Representation Theory Of Algebraic Groups And Quantum Groups

Author: Akihiko Gyoja
Publisher: Springer Science & Business Media
ISBN: 9780817646974
Size: 22.44 MB
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Invited articles by top notch experts Focus is on topics in representation theory of algebraic groups and quantum groups Of interest to graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics

Iterated Integrals And Cycles On Algebraic Manifolds

Author: Bruno Harris
Publisher: World Scientific
ISBN: 9812562575
Size: 18.71 MB
Format: PDF
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This subject has been of great interest both to topologists and tonumber theorists. The first part of this book describes some of thework of Kuo-Tsai Chen on iterated integrals and the fundamental groupof a manifold. The author attempts to make his exposition accessibleto beginning graduate students. He then proceeds to apply Chen''sconstructions to algebraic geometry, showing how this leads to someresults on algebraic cycles and the AbelOCoJacobihomomorphism. Finally, he presents a more general point of viewrelating Chen''s integrals to a generalization of the concept oflinking numbers, and ends up with a new invariant of homology classesin a projective algebraic manifold. The book is based on a coursegiven by the author at the Nankai Institute of Mathematics in the fallof 2001."

The Index Theorem And The Heat Equation Method

Author: Yanlin Yu
Publisher: World Scientific Publishing Company Incorporated
ISBN: 9789810246105
Size: 32.79 MB
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This book provides a self-contained representation of the local version of the Atiyah-Singer index theorem. It contains proofs of the Hodge theorem, the local index theorems for the Dirac operator and some first order geometric elliptic operators by using the heat equation method. The proofs are up to the standard of pure mathematics. In addition, a Chern root algorithm is introduced for proving the local index theorems, and it seems to be as efficient as other methods.

Minimal Submanifolds And Related Topics

Author: Y. L. Xin
Publisher: World Scientific
ISBN: 9789812564382
Size: 66.76 MB
Format: PDF, Mobi
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The Bernstein problem and the Plateau problem are central topics inthe theory of minimal submanifolds. This important book presents theDouglasOCoRado solution to the Plateau problem, but the main emphasisis on the Bernstein problem and its new developments in variousdirections: the value distribution of the Gauss image of a minimalsurface in Euclidean 3-space, Simons'' work for minimal graphichypersurfaces, and author''s own contributions to Bernstein typetheorems for higher codimension."

Protist Diversity And Geographical Distribution

Author: W. Foissner
Publisher: Springer Science & Business Media
ISBN: 9048128013
Size: 54.56 MB
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Conservation and biodiversity of protists The conservation of biodiversity is not just an issue of plants and vertebrates. It is the scarcely visible invertebrates and myriads of other microscopic organisms that are crucial to the maintenance of ecological processes on which all larger organisms and the composition of the atmosphere ultimately depend. Biodiversity and Conservation endeavours to take an holistic view of biodiversity, and when the opportunity arises to issue collections of papers dealing with too-often neglected groups of organisms. The protists, essentially eukaryotes that cannot be classi?ed in the kingdoms of animals, fungi, or plants, include some of the lea- known groups of organisms on earth. They are generally treated as a separate kingdom, commonly named Protista (or Protoctista) in textbooks, but in reality they are a mixture of organisms with disparate a?nities. Some authors have hypothesized that the numbers of protists are not especially large, and that many have extraordinarily wide distributions. However, the p- ture that unfolds from the latest studies discussed in this issue is di?erent. There are many species with wide ranges, and proportionately more cosmopolitan species than in macroorganism groups, as a result of their long evolutionary histories, but there are also de?nite patterns and geographical restrictions to be found. Further, some protists are linked to host organisms as mutualists or parasites and necessarily con?ned to the distributions of their hosts.