Basic number theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1974
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen
144 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 325 S. |
| ISBN: | 3540069356 0387069356 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV009056841 | ||
| 003 | DE-604 | ||
| 005 | 20080702 | ||
| 007 | t | ||
| 008 | 940227s1974 |||| 00||| eng d | ||
| 020 | |a 3540069356 |9 3-540-06935-6 | ||
| 020 | |a 0387069356 |9 0-387-06935-6 | ||
| 035 | |a (OCoLC)45571719 | ||
| 035 | |a (DE-599)BVBBV009056841 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-29T |a DE-384 |a DE-703 |a DE-739 |a DE-355 |a DE-Aug4 |a DE-91G |a DE-19 |a DE-188 | ||
| 082 | 0 | |a 512/.7 | |
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 100 | 1 | |a Weil, André |d 1906-1998 |e Verfasser |0 (DE-588)118980963 |4 aut | |
| 245 | 1 | 0 | |a Basic number theory |c André Weil |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1974 | |
| 300 | |a XVIII, 325 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen |v 144 | |
| 650 | 4 | |a Class field theory | |
| 650 | 4 | |a Number theory | |
| 650 | 0 | 7 | |a Zahlentheorie |0 (DE-588)4067277-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Zahlentheorie |0 (DE-588)4001170-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Klassenkörpertheorie |0 (DE-588)4030951-4 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4151278-9 |a Einführung |2 gnd-content | |
| 689 | 0 | 0 | |a Zahlentheorie |0 (DE-588)4067277-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Algebraische Zahlentheorie |0 (DE-588)4001170-7 |D s |
| 689 | 1 | |8 1\p |5 DE-604 | |
| 689 | 2 | 0 | |a Klassenkörpertheorie |0 (DE-588)4030951-4 |D s |
| 689 | 2 | |8 2\p |5 DE-604 | |
| 830 | 0 | |a Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen |v 144 |w (DE-604)BV000000395 |9 144 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005996000&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-005996000 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804123413952856065 |
|---|---|
| adam_text | Contents
Chronological table XII
Prerequisites and notations XIII
Table of notations XVII
PART I. ELEMENTARY THEORY
Chapter I. Locally compact fields 1
§1. Finite fields 1
§ 2. The module in a locally compact field 3
§3. Classification of locally compact fields 8
§4. Structure of ^-fields 12
Chapter II. Lattices and duality over local fields 24
§ 1. Norms 24
§2. Lattices 27
§3. Multiplicative structure of local fields 31
§ 4. Lattices over R 35
§ 5. Duality over local fields 38
Chapter III. Places of A-fields 43
§ 1. A-fields and their completions 43
§ 2. Tensor-products of commutative fields 48
§ 3. Traces and norms 52
§ 4. Tensor-products of A-fields and local fields 56
Chapter IV. Adeles 59
§1. Adeles of A-fields 59
§ 2. The main theorems 64
§3. Ideles 71
§4. Ideles of A-fields 75
X Contents
Chapter V. Algebraic number-fields 80
§ 1. Orders in algebras over Q 80
§2. Lattices over algebraic number-fields 81
§ 3. Ideals 85
§ 4. Fundamental sets 89
Chapter VI. The theorem of Riemann-Roch 96
Chapter VII. Zeta-functions of A-fields 102
§1. Convergence of Euler products 102
§ 2. Fourier transforms and standard functions 104
§3. Quasicharacters 114
§4. Quasicharacters of A-fields 118
§ 5. The functional equation 120
§ 6. The Dedekind zeta-function 127
§7. L-functions 130
§8. The coefficients of the L-series 134
Chapter VIII. Traces and norms 139
§1. Traces and norms in local fields 139
§2. Calculation of the different 143
§ 3. Ramification theory 147
§4. Traces and norms in A-fields 153
§5. Splitting places in separable extensions 158
§6. An application to inseparable extensions 159
PART II. CLASSFIELD THEORY
Chapter IX. Simple algebras 162
§ 1. Structure of simple algebras 162
§2. The representations of a simple algebra 168
§ 3. Factor-sets and the Brauer group 170
§4. Cyclic factor-sets 180
§ 5. Special cyclic factor-sets 185
Chapter X. Simple algebras over local fields 188
§1. Orders and lattices 188
§ 2. Traces and norms 193
§3. Computation of some integrals 195
Contents XI
Chapter XI. Simple algebras over A-fields 202
§ 1. Ramification 202
§ 2. The zeta-function of a simple algebra 203
§ 3. Norms in simple algebras . . . 206
§ 4. Simple algebras over algebraic number-fields 210
Chapter XII. Local classfield theory 213
§1. The formalism of classfield theory 213
§2. The Brauer group of a local field 220
§ 3. The canonical morphism 226
§4. Ramification of abelian extensions 230
§5. The transfer 240
Chapter XIII. Global classfield theory 244
§ 1. The canonical pairing 244
§ 2. An elementary lemma 250
§ 3. Hasse s law of reciprocity 252
§4. Classfield theory for Q 257
§ 5. The Hilbert symbol 260
§ 6. The Brauer group of an A-field 264
§7. The Hilbert p-symbol 267
§8. The kernel of the canonical morphism 271
§ 9. The main theorems 275
§10. Local behavior of abelian extensions 277
§11. Classical classfield theory 281
§ 12. Coronidis loco 288
Notes to the text 292
Appendix I. The transfer theorem 295
Appendix II. ^-groups for local fields 298
Appendix III. Shafarevitch s theorem 301
Appendix IV. The Herbrand distribution 308
Appendix V. Examples of L-Functions 313
Index of definitions 323
|
| any_adam_object | 1 |
| author | Weil, André 1906-1998 |
| author_GND | (DE-588)118980963 |
| author_facet | Weil, André 1906-1998 |
| author_role | aut |
| author_sort | Weil, André 1906-1998 |
| author_variant | a w aw |
| building | Verbundindex |
| bvnumber | BV009056841 |
| classification_rvk | SK 180 |
| ctrlnum | (OCoLC)45571719 (DE-599)BVBBV009056841 |
| dewey-full | 512/.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.7 |
| dewey-search | 512/.7 |
| dewey-sort | 3512 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02123nam a2200505 cb4500</leader><controlfield tag="001">BV009056841</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20080702 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">940227s1974 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540069356</subfield><subfield code="9">3-540-06935-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387069356</subfield><subfield code="9">0-387-06935-6</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)45571719</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV009056841</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-29T</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-Aug4</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.7</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 180</subfield><subfield code="0">(DE-625)143222:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Weil, André</subfield><subfield code="d">1906-1998</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)118980963</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Basic number theory</subfield><subfield code="c">André Weil</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">3. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">1974</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVIII, 325 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen</subfield><subfield code="v">144</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Class field theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Zahlentheorie</subfield><subfield code="0">(DE-588)4067277-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebraische Zahlentheorie</subfield><subfield code="0">(DE-588)4001170-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Klassenkörpertheorie</subfield><subfield code="0">(DE-588)4030951-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4151278-9</subfield><subfield code="a">Einführung</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Zahlentheorie</subfield><subfield code="0">(DE-588)4067277-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Algebraische Zahlentheorie</subfield><subfield code="0">(DE-588)4001170-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Klassenkörpertheorie</subfield><subfield code="0">(DE-588)4030951-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen</subfield><subfield code="v">144</subfield><subfield code="w">(DE-604)BV000000395</subfield><subfield code="9">144</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005996000&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-005996000</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| genre | (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV009056841 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:29:23Z |
| institution | BVB |
| isbn | 3540069356 0387069356 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005996000 |
| oclc_num | 45571719 |
| open_access_boolean | |
| owner | DE-29T DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-Aug4 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-188 |
| owner_facet | DE-29T DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-Aug4 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-188 |
| physical | XVIII, 325 S. |
| publishDate | 1974 |
| publishDateSearch | 1974 |
| publishDateSort | 1974 |
| publisher | Springer |
| record_format | marc |
| series | Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen |
| series2 | Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen |
| spelling | Weil, André 1906-1998 Verfasser (DE-588)118980963 aut Basic number theory André Weil 3. ed. Berlin [u.a.] Springer 1974 XVIII, 325 S. txt rdacontent n rdamedia nc rdacarrier Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen 144 Class field theory Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf Klassenkörpertheorie (DE-588)4030951-4 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Zahlentheorie (DE-588)4067277-3 s DE-604 Algebraische Zahlentheorie (DE-588)4001170-7 s 1\p DE-604 Klassenkörpertheorie (DE-588)4030951-4 s 2\p DE-604 Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen 144 (DE-604)BV000000395 144 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005996000&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Weil, André 1906-1998 Basic number theory Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen Class field theory Number theory Zahlentheorie (DE-588)4067277-3 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd Klassenkörpertheorie (DE-588)4030951-4 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4001170-7 (DE-588)4030951-4 (DE-588)4151278-9 |
| title | Basic number theory |
| title_auth | Basic number theory |
| title_exact_search | Basic number theory |
| title_full | Basic number theory André Weil |
| title_fullStr | Basic number theory André Weil |
| title_full_unstemmed | Basic number theory André Weil |
| title_short | Basic number theory |
| title_sort | basic number theory |
| topic | Class field theory Number theory Zahlentheorie (DE-588)4067277-3 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd Klassenkörpertheorie (DE-588)4030951-4 gnd |
| topic_facet | Class field theory Number theory Zahlentheorie Algebraische Zahlentheorie Klassenkörpertheorie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005996000&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT weilandre basicnumbertheory |