Leseprobe
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Étale Cohomology
James S. Milne
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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.
Kundenbewertungen
Finite morphism, Local ring, Diagram (category theory), Residue field, Finite field, Abelian category, Topological space, Affine variety, Cokernel, Base change, Category of sets, Algebraic space, Algebraically closed field, Henselian ring, Torsor (algebraic geometry), Topology, Intersection (set theory), Subset, Stein factorization, Direct limit, Profinite group, Zariski's main theorem, Cohomology, Cohomology ring, Algebraic cycle, Brauer group, Galois cohomology, Isomorphism class, Fibration, Principal homogeneous space, Galois extension, Lefschetz pencil, Commutative diagram, Morphism, Dedekind domain, Chow's lemma, Zariski topology, Existential quantification, Subcategory, Algebraic closure, Complex number, Noetherian, Theorem, Weil conjecture, Presheaf (category theory), Projection (mathematics), Closed immersion, G-module, Sheaf (mathematics), Fundamental group, Integral domain, Torsion sheaf, Group scheme, Algebraic equation, Functor, Subalgebra, Open set, Galois group, Yoneda lemma, Field of fractions, Projective variety, Vector bundle, Alexander Grothendieck, Sheaf of modules, Spectral sequence, Invertible sheaf, Subgroup, Surjective function, Codimension, Subring