Étale Cohomology

James S. Milne

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English

Princeton University Press
08 April 2025

Algebraic geometry; Analytic topology; History of mathematics

Series: Princeton Mathematical Series

An authoritative introduction to the essential features of étale cohomology

A. Grothendieck’s work on algebraic geometry is one of the most important mathematical achievements of the twentieth century. In the early 1960s, he and M. Artin introduced étale cohomology to extend the methods of sheaf-theoretic cohomology from complex varieties to more general schemes. This work found many applications, not only in algebraic geometry but also in several different branches of number theory and in the representation theory of finite and p-adic groups. In this classic book, James Milne provides an invaluable introduction to étale cohomology, covering the essential features of the theory.

Milne begins with a review of the basic properties of flat and étale morphisms and the algebraic fundamental group. He then turns to the basic theory of étale sheaves and elementary étale cohomology, followed by an application of the cohomology to the study of the Brauer group. After a detailed analysis of the cohomology of curves and surfaces, Milne proves the fundamental theorems in étale cohomology—those of base change, purity, Poincaré duality, and the Lefschetz trace formula—and applies these theorems to show the rationality of some very general L-series.

By: James S. Milne
Imprint: Princeton University Press
Country of Publication: United States
Dimensions: Height: 235mm, Width: 156mm,
ISBN: 9780691273792
ISBN 10: 0691273790
Series: Princeton Mathematical Series
Pages: 338
Publication Date: 08 April 2025
Audience: College/higher education , Further / Higher Education
Format: Hardback
Publisher's Status: Active

James S. Milne is professor emeritus of mathematics at the University of Michigan and recipient of the Steele Prize for Mathematical Exposition from the American Mathematical Society.