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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.
Sample Chapter(s)
Chapter 1: Descent Theory (476 KB)
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.
- 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)
