Etale cohomology theory
By: Lei Fu
Series: Nankai tracts in mathematics -- v. 13
Publisher: World Scientific
Published: 2011
Place of publication: Singapore; Hackensack, N.J
Language: eng
Number of pages: 611
ISBN-13: 9789814307727
Subjects: Homology theory
Notes: Includes bibliographical references (p. 607-608) and index.
Table of contents: title: Machine generated contents note: 1.Descent Theory; title: 1.1.Flat Modules; title: 1.2.Faithfully Flat Modules; title: 1.3.Local Criteria for Flatness; title: 1.4.Constructible Sets; title: 1.5.Flat Morphisms; title: 1.6.Descent of Quasi-coherent Sheaves; title: 1.7.Descent of Properties of Morphisms; title: 1.8.Descent of Schemes; title: 1.9.Quasi-finite Morphisms; title: 1.10.Passage to Limit; title: 2.Etale Morphisms and Smooth Morphisms; title: 2.1.The Sheaf of Relative Differentials; title: 2.2.Unramified Morphisms; title: 2.3.Etale Morphisms; title: 2.4.Smooth Morphisms; title: 2.5.Jacobian Criterion; title: 2.6.Infinitesimal Liftings of Morphisms; title: 2.7.Direct Limits and Inverse Limits; title: 2.8.Henselization; title: 2.9.Etale Morphisms between Normal Schemes; title: 3.Etale Fundamental Groups; title: 3.1.Finite Group Actions on Schemes; title: 3.2.Etale Covering Spaces and Fundamental Groups; title: 3.3.Functorial Properties of Fundamental Groups; title: 4.Group Cohomology and Galois Cohomology; title: 4.1.Group Cohomology; title: 4.2.Profinite Groups; title: 4.3.Cohomology of Profinite Groups; title: ^; title: 4.4.Cohomological Dimensions; title: 4.5.Galois Cohomology; title: 5.Etale Cohomology; title: 5.1.Presheavcs and Cech Cohomology; title: 5.2.Etale Sheaves; title: 5.3.Stalks of Sheaves; title: 5.4.Recollement of Sheaves; title: 5.5.The Functor f!; title: 5.6.Etale Cohomology; title: 5.7.Calculation of Etale Cohomology; title: 5.8.Constructible Sheaves; title: 5.9.Passage to Limit; title: 6.Derived Categories and Derived Functors; title: 6.1.Triangulated Categories; title: 6.2.Derived Categories; title: 6.3.Derived Functors; title: 6.4.RHom(-,-) and; title: &otimes;; title: 6.5.Way-out Functors; title: 7.Base Change Theorems; title: 7.1.Divisors; title: 7.2.Cohomology of Curves; title: 7.3.Proper Base Change Theorem; title: 7.4.Cohomology with Proper Support; title: 7.5.Cohomological Dimension of Rf; title: 7.6.Local Acyclicity; title: 7.7.Smooth Base Change Theorem; title: 7.8.Finiteness of Rf!; title: 8.Duality; title: 8.1.Extensions of Henselian Discrete Valuation Rings; title: 8.2.Trace Morphisms; title: 8.3.Duality for Curves; title: 8.4.The Functor Rf!; title: 8.5.Poincare Duality; title: 8.6.Cohomology Classes of Algebraic Cycles; title: ^; title: ^^; title: 9.Finiteness Theorems; title: 9.1.Sheaves with Group Actions; title: 9.2.Nearby Cycle and Vanishing Cycle; title: 9.3.Generic Base Change Theorem and Generic Local Acyclicity; title: 9.4.Finiteness of R&Psi;&eta;; title: 9.5.Finiteness Theorems; title: 9.6.Biduality; title: 10.l-adic Cohomology; title: 10.1.Adic Formalism; title: 10.2.Grothendieck-Ogg-Shafarevich Formula; title: 10.3.Frobenius Correspondences; title: 10.4.Lefschetz Trace Formula; title: 10.5.Grothendieck's Formula of L-functions.; title: ^^