Overview

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 CohomologyReadership: 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)

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