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基础数论 英文版PDF|Epub|txt|kindle电子书版本网盘下载
- AndreWeil编著 著
- 出版社： 世界图书北京出版公司
- ISBN：9787510004551
- 出版时间：2010
- 标注页数：316页
- 文件大小：15MB
- 文件页数：335页
- 主题词：数论－英文
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图书目录
PART Ⅰ．ELEMENTARY THEORY1
Chapter Ⅰ．Locally compact fields1
1．Finite fields1
2．The module in a locally compact field3
3．Classification of locally compact fields8
4．Structure of p-fields12
Chapter Ⅱ．Lattices and duality over local fields24
1．Norms24
2．Lattices27
3．Multiplicative structure of local fields31
4．Lattices over R35
5．Duality over local fields38
Chapter Ⅲ．Places of A-fields43
1．A-fields and their completions43
2．Tensor-products of commutative fields48
3．Traces and norms52
4．Tensor-products of A-fields and local fields56
Chapter Ⅳ．Adeles59
1．Adeles of A-fields59
2．The main theorems64
3．Ideles71
4．Ideles of A-fields75
Chapter Ⅴ．Algebraic number-fields80
1．Orders in algebras over Q80
2．Lattices over algebraic number-fields81
3．Ideals85
4．Fundamental sets89
Chapter Ⅵ．The theorem of Riemann-Roch96
Chapter Ⅶ．Zeta-functions of A-fields102
1．Convergence of Euler products102
2．Fourier transforms and standard functions104
3．Quasicharacters114
4．Quasicharacters of A-fields118
5．The functional equation120
6．The Dedekind zeta-function127
7．L-functions130
8．The coefficients of the L-series134
Chapter Ⅷ．Traces and norms139
1．Traces and norms in local fields139
2．Calculation of the different143
3．Ramification theory147
4．Traces and norms in A-fields153
5．Splitting places in separable extensions158
6．An application to inseparable extensions159
PART Ⅱ．CLASSFIELD THEORY162
Chapter Ⅸ．Simple algebras162
1．Structure of simple algebras162
2．The representations of a simple algebra168
3．Factor-sets and the Brauer group170
4．Cyclic factor-sets180
5．Special cyclic factor-sets185
Chapter Ⅹ．Simple algebras over local fields188
1．Orders and lattices188
2．Traces and norms193
3．Computation of some integrals195
Chapter Ⅺ．Simple algebras over A-fields202
1．Ramification202
2．The zeta-function of a simple algebra203
3．Norms in simple algebras206
4．Simple algebras over algebraic number-fields210
Chapter Ⅻ．Local classfield theory213
1．The formalism of classfield theory213
2．The Brauer group of a local field220
3．The canonical morphism226
4．Ramification of abelian extensions230
5．The transfer240
Chapter ⅩⅢ．Global classfield theory244
1．The canonical pairing244
2．An elementary lemma250
3．Hasse's"law of reciprocity"252
4．Classfield theory for Q257
5．The Hilbert symbol260
6．The Brauer group of an A-field264
7．The Hilbert p-symbol267
8．The kernel of the canonical morphism271
9．The main theorems275
10．Local behavior of abelian extensions277
11．"Classical"classfield theory281
12．"Coronidis loco"288
Notes to the text292
Appendix Ⅰ．The transfer theorem295
Appendix Ⅱ．W-groups for local fields298
Appendix Ⅲ．Shafarevitch's theorem301
Appendix Ⅳ．The Herbrand distribution308