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Books, Free Shipping, Basic Number Theory

Posted at: Offers to Sell and Export | Posted on: Mon 12 Jul, 2010 8:52 am | Product Category: Reference books [3760]
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Product Description:

The first part of this volume is based on a course taught at Princeton University

in 1961-62; at that time, an excellent set of notes was prepared by David Cantor, and it was originally my intention to make these notes available to the mathematical public with only quite minor changes. Then, among some old papers of mine, I accidentally came across a long forgotten manuscript by Coevally, of prewar vintage (forgotten, that is to say, both by me and by its author) which, to my taste at least, seemed to have aged very well. It contained a brief but essentially complete account of the main features of class field theory, both local and global; and it soon became obvious that the usefulness of the intended volume would be greatly enhanced if I included such a treatment of this topic. It had to be expanded, in accordance with my own plans, but its outline could be preserved without much change. In fact, I have adhered to it rather closely at some critical points.


Chronological table

Prerequisites and notations

Table of notations

Part i elementary theory

 Chapter I Locally compact fields

  1 Finite fields

  2 The module in a locally compact field

  3 Classification of locally compact fields

  4 Structure 0fp-fields

 Chapter II Lattices and duality over local fields

  1 Norms

  2 Lattices

  3 Multiplicative structure of local fields

  4 Lattices over R

  5 Duality over local fields

 Chapter III Places of A-fields

  1 A-fields and their completions

  2 Tensor-products of commutative fields

  3 Traces and norms

  4 Tensor-products of A-fields and local fields

 Chapter IV Adeles

  1 Adeles of A-fields

  2 The main theorems

  3 Ideles

   4 Ideles of A-fields

 Chapter V Algebraic number-fields

  1, Orders in algebras over Q

  2 Lattices over algebraic number-fields

  3 Ideals

  4 Fundamental sets

 Chapter VI The theorem of Riemann-Roch

 Chapter VII Zeta-functions of A-fields

  1 Convergence of Euler products

  2 Fourier transforms and standard functions

  3 Quasicharacters

  4 Quasicharacters of A-fields

  5 The functional equation

  6 The Dedekind zeta-function

  7 L-functions

  8 The coefficients of the L-series

 Chapter VIII Traces and norms

  1 Traces and norms in local fields

  2 Calculation of the different

  3 Ramification theory

  4 Traces and norms in A-fields

  5 Splitting places in separable extensions

  6 An application to inseparable extensions

Part ii classfield theory

 Chapter IX Simple algebras

  1 Structure of simple algebras

  2 The representations of a simple algebra

  3 Factor-sets and the Brauer group

  4 Cyclic factor-sets

  5 Special cyclic factor-sets

 Chapter X Simple algebras over local fields

  1 Orders and lattices

  2 Traces and norms

  3 Computation of some integrals

Product Details

Author Andre Weil

Publisher World Publishing Corporation

Isbn 9787510004551, 7510004551

Published January 2010

Pages 312

Size 24k

Edition First

Format Paperback

Language English

Page material gelatine plate paper

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