Ebook: Basic Number Theory
Author: Professor André Weil (auth.)
- Tags: Number Theory
- Series: Classics in Mathematics 144
- Year: 1974
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 3
- Language: English
- pdf
)tPI(}jlOV, e~oxov (10CPUljlr1.'CWV Aiux., llpop. . .dsup.. 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 Chevalley, of pre-war 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 com plete account of the main features of classfield 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.
Elementary Theory: Locally compact fields.- Lattices and duality over local fields.- Places of A-fields.- Adeles.- Algebraic number fields.- The theorem of Riemann-Roch.- Zeta-functions of A-fields.- Traces and norms.- ClassfieldTheory: Simple algebras.- Simple algebras over local fields.- Simple algebras over A-fields.- Local classfield theory.- Global classfield theory.
Elementary Theory: Locally compact fields.- Lattices and duality over local fields.- Places of A-fields.- Adeles.- Algebraic number fields.- The theorem of Riemann-Roch.- Zeta-functions of A-fields.- Traces and norms.- ClassfieldTheory: Simple algebras.- Simple algebras over local fields.- Simple algebras over A-fields.- Local classfield theory.- Global classfield theory.
Content:
Front Matter....Pages I-XVIII
Locally compact fields....Pages 1-23
Lattices and duality over local fields....Pages 24-42
Places of A-fields....Pages 43-58
Adeles....Pages 59-79
Algebraic number-fields....Pages 80-95
The theorem of Riemann-Roch....Pages 96-101
Zeta-functions of A-fields....Pages 102-138
Traces and norms....Pages 139-161
Simple algebras....Pages 162-187
Simple algebras over local fields....Pages 188-201
Simple algebras over A-fields....Pages 202-212
Local classfield theory....Pages 213-243
Global classfield theory....Pages 244-289
Back Matter....Pages 292-316
Elementary Theory: Locally compact fields.- Lattices and duality over local fields.- Places of A-fields.- Adeles.- Algebraic number fields.- The theorem of Riemann-Roch.- Zeta-functions of A-fields.- Traces and norms.- ClassfieldTheory: Simple algebras.- Simple algebras over local fields.- Simple algebras over A-fields.- Local classfield theory.- Global classfield theory.
Content:
Front Matter....Pages I-XVIII
Locally compact fields....Pages 1-23
Lattices and duality over local fields....Pages 24-42
Places of A-fields....Pages 43-58
Adeles....Pages 59-79
Algebraic number-fields....Pages 80-95
The theorem of Riemann-Roch....Pages 96-101
Zeta-functions of A-fields....Pages 102-138
Traces and norms....Pages 139-161
Simple algebras....Pages 162-187
Simple algebras over local fields....Pages 188-201
Simple algebras over A-fields....Pages 202-212
Local classfield theory....Pages 213-243
Global classfield theory....Pages 244-289
Back Matter....Pages 292-316
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