Étale Cohomology (PMS-33), Volume 33 /

Étale Cohomology (PMS-33), Volume 33 / / James S. Milne.

One of the most important mathematical achievements of the past several decades has been A. Grothendieck's work on algebraic geometry. In the early 1960s, he and M. Artin introduced étale cohomology in order to extend the methods of sheaf-theoretic cohomology from complex varieties to more gene...

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Superior document:Title is part of eBook package: De Gruyter Princeton Mathematical Series eBook Package
VerfasserIn:
Milne, James S.,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2016]
©1980
Year of Publication:2016
Language:English
Series:Princeton Mathematical Series ; 5656
Online Access:
Physical Description:1 online resource (344 p.)
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100 1 |a Milne, James S.,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Étale Cohomology (PMS-33), Volume 33 /  |c James S. Milne. 
264 1 |a Princeton, NJ :   |b Princeton University Press,   |c [2016] 
264 4 |c ©1980 
300 |a 1 online resource (344 p.) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
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490 0 |a Princeton Mathematical Series ;  |v 5656 
505 0 0 |t Frontmatter --   |t Contents --   |t Preface --   |t Terminology and Conventions --   |t Chapter I. Étale Morphisms --   |t Chapter II. Sheaf Theory --   |t Chapter III. Cohomology --   |t Chapter IV. The Brauer Group --   |t Chapter V. The Cohomology of Curves and Surfaces --   |t Chapter VI. The Fundamental Theorems --   |t Appendix A. Limits --   |t Appendix B. Spectral Sequences --   |t Appendix C. Hypercohomology --   |t Bibliography --   |t Index 
506 0 |a restricted access  |u http://purl.org/coar/access_right/c_16ec  |f online access with authorization  |2 star 
520 |a One of the most important mathematical achievements of the past several decades has been A. Grothendieck's work on algebraic geometry. In the early 1960s, he and M. Artin introduced étale cohomology in order 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. Yet until now, the work has been available only in the original massive and difficult papers. In order to provide an accessible introduction to étale cohomology, J. S. Milne offers this more elementary account covering the essential features of the theory. The author begins with a review of the basic properties of flat and étale morphisms and of the algebraic fundamental group. The next two chapters concern the basic theory of étale sheaves and elementary étale cohomology, and are 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, Professor Milne proves the fundamental theorems in étale cohomology -- those of base change, purity, Poincaré duality, and the Lefschetz trace formula. He then applies these theorems to show the rationality of some very general L-series.Originally published in 1980.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. 
530 |a Issued also in print. 
538 |a Mode of access: Internet via World Wide Web. 
546 |a In English. 
588 0 |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) 
650 0 |a Geometry, Algebraic. 
650 0 |a Homology theory. 
650 0 |a Sheaf theory. 
650 7 |a MATHEMATICS / Topology.  |2 bisacsh 
653 |a Abelian category. 
653 |a Abelian group. 
653 |a Adjoint functors. 
653 |a Affine variety. 
653 |a Alexander Grothendieck. 
653 |a Algebraic closure. 
653 |a Algebraic cycle. 
653 |a Algebraic equation. 
653 |a Algebraic space. 
653 |a Algebraically closed field. 
653 |a Artinian. 
653 |a Automorphism. 
653 |a Base change. 
653 |a Brauer group. 
653 |a CW complex. 
653 |a Cardinal number. 
653 |a Category of sets. 
653 |a Central simple algebra. 
653 |a Chow's lemma. 
653 |a Closed immersion. 
653 |a Codimension. 
653 |a Cohomology ring. 
653 |a Cohomology. 
653 |a Cokernel. 
653 |a Commutative diagram. 
653 |a Complex number. 
653 |a Dedekind domain. 
653 |a Derived category. 
653 |a Diagram (category theory). 
653 |a Direct limit. 
653 |a Discrete valuation ring. 
653 |a Divisor. 
653 |a Epimorphism. 
653 |a Equivalence class. 
653 |a Existential quantification. 
653 |a Fibration. 
653 |a Field of fractions. 
653 |a Fine topology (potential theory). 
653 |a Finite field. 
653 |a Finite morphism. 
653 |a Flat morphism. 
653 |a Functor. 
653 |a Fundamental class. 
653 |a Fundamental group. 
653 |a G-module. 
653 |a Galois cohomology. 
653 |a Galois extension. 
653 |a Galois group. 
653 |a Generic point. 
653 |a Group scheme. 
653 |a Gysin sequence. 
653 |a Henselian ring. 
653 |a Identity element. 
653 |a Inclusion map. 
653 |a Integral domain. 
653 |a Intersection (set theory). 
653 |a Inverse limit. 
653 |a Invertible sheaf. 
653 |a Isomorphism class. 
653 |a Lefschetz pencil. 
653 |a Local ring. 
653 |a Maximal ideal. 
653 |a Module (mathematics). 
653 |a Morphism of schemes. 
653 |a Morphism. 
653 |a Noetherian. 
653 |a Open set. 
653 |a Power series. 
653 |a Presheaf (category theory). 
653 |a Prime ideal. 
653 |a Prime number. 
653 |a Principal homogeneous space. 
653 |a Profinite group. 
653 |a Projection (mathematics). 
653 |a Projective variety. 
653 |a Quasi-compact morphism. 
653 |a Residue field. 
653 |a Riemann surface. 
653 |a Sheaf (mathematics). 
653 |a Sheaf of modules. 
653 |a Special case. 
653 |a Spectral sequence. 
653 |a Stein factorization. 
653 |a Subalgebra. 
653 |a Subcategory. 
653 |a Subgroup. 
653 |a Subring. 
653 |a Subset. 
653 |a Surjective function. 
653 |a Tangent space. 
653 |a Theorem. 
653 |a Topological space. 
653 |a Topology. 
653 |a Torsion sheaf. 
653 |a Torsor (algebraic geometry). 
653 |a Vector bundle. 
653 |a Weil conjecture. 
653 |a Yoneda lemma. 
653 |a Zariski topology. 
653 |a Zariski's main theorem. 
773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton Mathematical Series eBook Package  |z 9783110501063  |o ZDB-23-PMS 
773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton University Press Complete eBook-Package 2016  |z 9783110638592 
776 0 |c print  |z 9780691082387 
856 4 0 |u https://doi.org/10.1515/9781400883981 
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