Record Nr.

UNINA9910811765303321

Autore

Moreno Carlos J.

Titolo

Advanced analytic number theory . Part 1 Ramification theoretic methods / / Carlos J. Moreno

Pubbl/distr/stampa


Providence, Rhode Island : , : American Mathematical Society, , [1983]
©1983

ISBN

0-8218-7601-5

Descrizione fisica

1 online resource (202 p.)

Collana

Contemporary mathematics, , 0271-4132 ; ; 15

Disciplina

512/.7

Soggetti

Number theory

Algebraic fields

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

""Contents""; ""Preface""; ""Chapter 0. Introduction""; ""Â1. A historical perspective""; ""Â2. The explicit formulas: motivation""; ""Chapter I. Galois Theory for Infinite Extensions""; ""Â1. Fundamental Theorem of Galois Theory for infinite extensions""; ""Â2. Topological properties of Gal(K'/K)""; ""Â3. Example""; ""Chapter II. Projective Limits""; ""Â1. Basic definitions""; ""Â2. Examples""; ""Â3. Homomorphisms""; ""Chapter III. Elementary Theory of l-adic Integration""; ""Â1. Distributions and measures""; ""Â2. Measures on groups""; ""Â3. Riemann sums""

""Â4. l-adic Haar measures""""Â5. Examples""; ""Chapter IV. Ramification Theory""; ""Â1. The v-function""; ""Â2. Transitivity properties of the v-function""; ""Â3. The different""; ""Â4. Transitivity properties of the different""; ""Â5. Complementary basis""; ""Â6. Fundamental inequality and the C-invariant""; ""Â7. Quotients of Galois groups and Herbrand's Theorem""; ""Chapter V. Multiplicative versus Additive Reduction""; ""Â1. The case of a local field""; ""Â2. The module structure of the unit group""; ""Â3. The case of an elliptic curve""

""Chapter VI. Ramification of Abelian Extensions""""Â1. Index computations""; ""Â2. Main Theorem""; ""Chapter VII. The Weil Groups of a Local Field""; ""Â1. The Frobenius automorphism""; ""Â2. The relative Weil group of a non-archimedean local field""; ""Â3. The absolute Weil group""; ""Â4. The Weil group of an archimedean local field""; ""Â5. The Weil-Deligne group""; ""Appendix: The non-abelian

local reciprocity law""; ""Chapter VIII. Shafarevitch's Theorem""; ""Â1. Representations of a simple algebra""; ""Â2. Factor sets""; ""Â3. Subalgebras of central simple algebras""

""Â4. Cyclic algebras""""Â5. Algebras and group extensions""; ""Â6. Powers of central simple algebras""; ""Â7. Generators of the Brauer group""; ""Â8. Structure of the relative Weil group""; ""Â9. Shafarevitch's Theorem""; ""Appendix: I. The Brauer group of central 'simple algebras over K""; ""II. The group H2(G,Kxs)""; ""Chapter IX. The Herbrand Distribution""; ""Â1. The Herbrand distribution: definition and basic facts""; ""Â2. The support of the Herbrand distribution""; ""Â3. Determination of the Herbrand distribution on Gal(Kab/K)""

""Â4. Functoriality properties of the Herbrand distribution""""Â5. The Herbrand distribution and measures on the Weil group""; ""Â6. The integral formula for the Herbrand distribution""; ""Â7. Conductors, the Artin representation, and the Herbrand distribution""; ""Bibliography""; ""Index""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""L""; ""M""; ""P""; ""R""; ""S""; ""T""; ""w""