Milne etale cohomology

Algebraic geometry

"The purpose of this book is to provide a comprehensive introduction ot the étale topology, sheaf theory, and cohomology... The étale topology was initially defined by A. Grothendieck and developed by him with the aid of M. Artin and J.-L. Verdier in order to explain Weil's insight that, for polynomial equations with integer coefficients, the complex topology of the set of complex solutions of the equations should profoundly influence the number of solutions of the equations modulo a prime number. In this, the étale topology has been brilliantly successful."

Chapter I. Étale Morphisms Edit

Section I.1. Finite and Quasi-Finite Morphisms Edit

  • If, moreover, $ \Gamma(f^{-1}(U), \mathcal{O}_y) $ is a finite $ \Gamma(U, \mathcal{O}_X) $-algebra...: i.e. if the former is finitely generated as a module over the latter.
  • ... and let L be a finite field extension of R(x)...: i.e. a finite-dimensional extension.

Section I.2. Flat Morphisms Edit

Section I.3. Étale Morphisms Edit

Section I.4. Henselian Rings Edit

Section I.5. The Fundamental Group: Galois Coverings Edit

Chapter II. Sheaf Theory Edit

Chapter III. Cohomology Edit

Chapter IV. The Brauer Group Edit

Chapter V. Cohomology of Curves and Surfaces Edit

Chapter VI. The Fundamental Theorems Edit