Etale Cohomology Theory

Revised Edition

Nonfiction, Science & Nature, Mathematics, Geometry, Algebra
Cover of the book Etale Cohomology Theory by Lei Fu, World Scientific Publishing Company
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Author: Lei Fu ISBN: 9789814675109
Publisher: World Scientific Publishing Company Publication: February 27, 2015
Imprint: WSPC Language: English
Author: Lei Fu
ISBN: 9789814675109
Publisher: World Scientific Publishing Company
Publication: February 27, 2015
Imprint: WSPC
Language: English

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 Theory
  • Etale Morphisms and Smooth Morphisms
  • Etale Fundamental Groups
  • Group Cohomology and Galois Cohomology
  • Etale Cohomology
  • Derived Categories and Derived Functors
  • Base Change Theorems
  • Duality
  • Finiteness Theorems
  • ℓ-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 theory
  • To 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)
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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:

Readership: Graduate students and researchers in pure mathematics.
Key Features:

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