Étale Cohomology (eBook)

James S. Milne (Autor)

eBook Download: EPUB

2025
580 Seiten
Princeton University Press (Verlag)
978-0-691-27377-8 (ISBN)

Infos

An authoritative introduction to the essential features of etale cohomologyA. 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 etale 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 etale cohomology, covering the essential features of the theory.Milne begins with a review of the basic properties of flat and etale morphisms and the algebraic fundamental group. He then turns to the basic theory of etale sheaves and elementary etale 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 etale cohomologythose of base change, purity, Poincare duality, and the Lefschetz trace formulaand applies these theorems to show the rationality of some very general L-series.

Produkt-Details

• Erscheint lt. Verlag: 8.4.2025
• Reihe/Serie: Princeton Legacy Library
• Reihe/Serie: Princeton Mathematical Series
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
• Schlagworte: Abelian category • affine variety • Alexander Grothendieck • Algebraically closed field • algebraic closure • algebraic cycle • algebraic equation • Algebraic space • Base change • Brauer group • Category of sets • Chow's lemma • Closed immersion • Codimension • cohomology • Cohomology ring • Cokernel • Commutative diagram • complex number • Dedekind domain • Diagram (category theory) • Direct limit • existential quantification • fibration • Field of fractions • finite field • Finite morphism • functor • fundamental group • galois cohomology • Galois extension • Galois group • G-module • group scheme • Henselian ring • integral domain • Intersection (set theory) • Invertible sheaf • isomorphism class • Lefschetz pencil • Local ring • Morphism • Noetherian • Open set • Presheaf (category theory) • Principal homogeneous space • Profinite group • Projection (mathematics) • projective variety • residue field • Sheaf (mathematics) • sheaf of modules • Spectral Sequence • Stein factorization • Subalgebra • subcategory • SUBGROUP • Subring • Subset • Surjective function • Theorem • Topological space • Topology • Torsion sheaf • Torsor (algebraic geometry) • vector bundle • Weil conjecture • Yoneda Lemma • Zariski's main theorem • Zariski topology
• ISBN-10: 0-691-27377-4 / 0691273774
• ISBN-13: 978-0-691-27377-8 / 9780691273778