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Etale Cohomology Theory : Nankai Tracts in Mathematics - Lei Fu

Etale Cohomology Theory

Nankai Tracts in Mathematics

By: Lei Fu


Published: 15th March 2011
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New Edition available hereEtale 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.

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 "Mathematical Reviews" The book will certainly be very useful to anybody wishing to understand the key tools and results in tale cohomology theory, together with their proofs Any reader with adequate background and an interest in seriously studying tale cohomology will find the thoroughness of this book really useful. -- MathSciNet "MathSciNet"

Prefacep. v
Descent Theoryp. 1
Flat Modulesp. 1
Faithfully Flat Modulesp. 3
Local Criteria for Flatnessp. 10
Constructible Setsp. 15
Flat Morphismsp. 18
Descent of Quasi-coherent Sheavesp. 21
Descent of Properties of Morphismsp. 28
Descent of Schemesp. 35
Quasi-finite Morphismsp. 41
Passage to Limitp. 45
Etale Morphisms and Smooth Morphismsp. 59
The Sheaf of Relative Differentialsp. 59
Unramified Morphismsp. 64
Etale Morphismsp. 66
Smooth Morphismsp. 73
Jacobian Criterionp. 75
Infinitesimal Liftings of Morphismsp. 83
Direct Limits and Inverse Limitsp. 87
Henselizationp. 90
Etale Morphisms between Normal Schemesp. 113
Etale Fundamental Groupsp. 117
Finite Group Actions on Schemesp. 117
Etale Covering Spaces and Fundamental Groupsp. 121
Functorial Properties of Fundamental Groupsp. 131
Group Cohomology and Galois Cohomologyp. 139
Group Cohomologyp. 139
Profinite Groupsp. 146
Cohomology of Profinite Groupsp. 152
Cohomological Dimensionsp. 161
Galois Cohomologyp. 164
Etale Cohomologyp. 171
Presheaves and Cech Cohomologyp. 171
Etale Sheavesp. 176
Stalks of Sheavesp. 193
Recollement of Sheavesp. 201
The Functor f!p. 205
Etale Cohomologyp. 210
Calculation of Etale Cohomologyp. 222
Constructible Sheavesp. 245
Passage to Limitp. 257
Derived Categories and Derived Functorsp. 267
Triangulated Categoriesp. 267
Derived Categoriesp. 272
Derived Functorsp. 279
RHom(-, -) and - ⊗LA -p. 287
Way-out Functorsp. 303
Base Change Theoremsp. 311
Divisorsp. 311
Cohomology of Curvesp. 317
Proper Base Change Theoremp. 331
Cohomology with Proper Supportp. 350
Cohomological Dimension of Rf*p. 368
Local Acyclicityp. 377
Smooth Base Change Theoremp. 391
Finiteness of Rf!p. 406
Dualityp. 411
Extensions of Henselian Discrete Valuation Ringsp. 411
Trace Morphismsp. 419
Duality for Curvesp. 432
The Functor Rf!p. 443
Poincaré Dualityp. 462
Cohomology Classes of Algebraic Cyclesp. 478
Finiteness Theoremsp. 497
Sheaves with Group Actionsp. 497
Nearby Cycle and Vanishing Cyclep. 502
Generic Base Change Theorem and Generic Local Acyclicityp. 509
Finiteness of R¿¿p. 517
Finiteness Theoremsp. 521
Bidualityp. 526
l-adic Cohomologyp. 531
Adic Formalismp. 531
Grothendieck-Ogg-Shafarevich Formulap. 566
Frobenius Correspondencesp. 585
Lefschetz Trace Formulap. 592
Grothendieck's Formula of L-functionsp. 603
Bibliographyp. 607
Indexp. 609
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9789814307727
ISBN-10: 9814307726
Series: Nankai Tracts in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 624
Published: 15th March 2011
Publisher: World Scientific Publishing Co Pte Ltd
Country of Publication: SG
Dimensions (cm): 22.86 x 15.24  x 3.81
Weight (kg): 1.02