Profinite Groups, Arithmetic, and Geometry. (AM-67), Volume 67 / / Stephen S. Shatz

• Autore: Shatz Stephen S.
• Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2016]; ©1972
• Descrizione fisica: 1 online resource (265 pages)
• Disciplina: 512/.2
• Soggetto topico: Homology theory; Finite groups; Algebraic number theory
• Soggetto non controllato: Abelian group; Alexander Grothendieck; Algebraic closure; Algebraic extension; Algebraic geometry; Algebraic number field; Brauer group; Category of abelian groups; Category of sets; Characterization (mathematics); Class field theory; Cohomological dimension; Cohomology; Cokernel; Commutative diagram; Composition series; Computation; Connected component (graph theory); Coset; Cup product; Dedekind domain; Degeneracy (mathematics); Diagram (category theory); Dimension (vector space); Diophantine geometry; Discrete group; Equivalence of categories; Exact sequence; Existential quantification; Explicit formula; Exponential function; Family of sets; Field extension; Finite group; Fundamental class; G-module; Galois cohomology; Galois extension; Galois group; Galois module; Galois theory; General topology; Geometry; Grothendieck topology; Group cohomology; Group extension; Group scheme; Group theory; Hilbert symbol; Hopf algebra; Ideal (ring theory); Inequality (mathematics); Injective sheaf; Inner automorphism; Inverse limit; Kummer theory; Lie algebra; Linear independence; Local field; Mathematical induction; Mathematician; Mathematics; Module (mathematics); Morphism; Natural topology; Neighbourhood (mathematics); Normal extension; Normal subgroup; Number theory; P-adic number; P-group; Polynomial; Pontryagin duality; Power series; Prime number; Principal ideal; Profinite group; Quadratic reciprocity; Quotient group; Ring of integers; Sheaf (mathematics); Special case; Subcategory; Subgroup; Supernatural number; Sylow theorems; Tangent space; Theorem; Topological group; Topological property; Topological ring; Topological space; Topology; Torsion group; Torsion subgroup; Transcendence degree; Triviality (mathematics); Unique factorization domain; Variable (mathematics); Vector space
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Frontmatter -- PREFACE -- CONTENTS -- CHAPTER I. PROFINITE GROUPS -- CHAPTER II. COHOMOLOGY OF PROFINITE GROUPS -- CHAPTER III. COHOMOLOGICAL DIMENSION -- CHAPTER IV. GALOIS COHOMOLOGY AND FIELD THEORY -- CHAPTER V. LOCAL CLASS FIELD THEORY -- CHAPTER VI. DUALITY -- BIBLIOGRAPHY
• Sommario/riassunto: In this volume, the author covers profinite groups and their cohomology, Galois cohomology, and local class field theory, and concludes with a treatment of duality. His objective is to present effectively that body of material upon which all modern research in Diophantine geometry and higher arithmetic is based, and to do so in a manner that emphasizes the many interesting lines of inquiry leading from these foundations.
• Titolo autorizzato: Profinite Groups, Arithmetic, and Geometry. (AM-67), Volume 67
• ISBN: 1-4008-8185-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910154751103321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; Number 67.