Étale Cohomology (eBook)

James S. Milne (Autor)

eBook Download: PDF

2016
344 Seiten
Princeton University Press (Verlag)
978-1-4008-8398-1 (ISBN)

Infos

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 etale 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 etale 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 etale morphisms and of the algebraic fundamental group. The next two chapters concern the basic theory of etale sheaves and elementary etale 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 etale cohomology -- those of base change, purity, Poincare 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.

Autor

J. S. Milne is Professor Emeritus of Mathematics at the University of Michigan at Ann Arbor.

Produkt-Details

• Erscheint lt. Verlag: 11.10.2016
• Reihe/Serie: Princeton Legacy Library
• Reihe/Serie: Princeton Legacy Library
• Reihe/Serie: Princeton Mathematical Series
• Reihe/Serie: Princeton Mathematical Series
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
• Schlagworte: Abelian category • abelian group • Adjoint functors • affine variety • Alexander Grothendieck • Algebraically closed field • algebraic closure • algebraic cycle • algebraic equation • Algebraic space • Artinian • automorphism • Base change • Brauer group • cardinal number • Category of sets • Central simple algebra • Chow's lemma • Closed immersion • Codimension • cohomology • Cohomology ring • Cokernel • Commutative diagram • complex number • CW complex • Dedekind domain • derived category • Diagram (category theory) • Direct limit • Discrete valuation ring • Divisor • Epimorphism • equivalence class • existential quantification • fibration • Field of fractions • Fine topology (potential theory) • finite field • Finite morphism • Flat morphism • functor • Fundamental class • fundamental group • galois cohomology • Galois extension • Galois group • Generic point • G-module • group scheme • Gysin sequence • Henselian ring • Identity element • Inclusion map • integral domain • Intersection (set theory) • Inverse limit • Invertible sheaf • isomorphism class • Lefschetz pencil • Local ring • Maximal Ideal • Module (mathematics) • Morphism • Morphism of schemes • Noetherian • Open set • power series • Presheaf (category theory) • Prime Ideal • Prime number • Principal homogeneous space • Profinite group • Projection (mathematics) • projective variety • Quasi-compact morphism • residue field • Riemann surface • Sheaf (mathematics) • sheaf of modules • Special case • Spectral Sequence • Stein factorization • Subalgebra • subcategory • SUBGROUP • Subring • Subset • Surjective function • Tangent Space • Theorem • Topological space • Topology • Torsion sheaf • Torsor (algebraic geometry) • vector bundle • Weil conjecture • Yoneda Lemma • Zariski's main theorem • Zariski topology
• ISBN-10: 1-4008-8398-9 / 1400883989
• ISBN-13: 978-1-4008-8398-1 / 9781400883981