Algebraic number theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1999
|
| Series: | Grundlehren der mathematischen Wissenschaften
322 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xvii, 571 Seiten |
| ISBN: | 3540653996 9783540653998 |
Staff View
MARC
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| 100 | 1 | |a Neukirch, Jürgen |d 1937-1997 |0 (DE-588)117716839 |4 aut | |
| 240 | 1 | 0 | |a Algebraische Zahlentheorie |
| 245 | 1 | 0 | |a Algebraic number theory |c Jürgen Neukirch. Transl. from the German by Norbert Schappacher |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1999 | |
| 300 | |a xvii, 571 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Grundlehren der mathematischen Wissenschaften |v 322 | |
| 650 | 0 | 7 | |a Algebraische Zahlentheorie |0 (DE-588)4001170-7 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804127151082962944 |
|---|---|
| adam_text | Table
of
Contents
Chapter I: Algebraic Integers
....................1
§ 1.
The Gaussian Integers
...................... 1
§ 2.
Integrality
...........................5
§ 3.
Ideals
............................. 16
§ 4.
Lattices
............................ 23
§ 5.
Minkowski Theory
...................... 28
§ 6.
The Class Number
....................... 34
§ 7.
Dirichlet s Unit Theorem
.................... 39
§ 8.
Extensions of Dedekind Domains
................ 44
§ 9.
Hubert s Ramification Theory
................. 53
§ 10.
Cyclotomic Fields
...................... 58
§11.
Localization
......................... 65
§ 12.
Orders
............................ 72
§ 13.
One-dimensional Schemes
.................. 84
§ 14.
Function Fields
....................... 94
Chapter II: The Theory of Valuations
............... 99
§ 1.
The
p-aåic
Numbers
......................99
§ 2.
The p-adic Absolute Value
...................106
§ 3.
Valuations
..........................116
§ 4.
Completions
.........................123
§ 5.
Local Fields
..........................134
§ 6.
Henselian Fields
........................143
§ 7.
Unramified and Tamely Ramified Extensions
..........152
§ 8.
Extensions of Valuations
....................160
§ 9.
Galois Theory of Valuations
..................166
§ 10.
Higher Ramification Groups
................- 176
Chapter III: Riemann-Roch Theory
...............183
§ 1.
Primes
............................183
§ 2.
Different and Discriminant
...................194
§ 3.
Riemann-Roch
........................208
§ 4.
Metrized o-Modules
......................224
xvi
Table of Contents
§ 5.
Grothendieck Groups
.....................233
§ 6.
The Chern Character
......................243
§ 7.
Grothendieck-Riemann-Roch
.................246
§ 8.
The Euler-Minkowski Characteristic
..............255
Chapter IV: Abstract Class Field Theory
.............261
§ 1.
Infinite Galois Theory
.....................261
§ 2.
Projective
and Inductive Limits
.................265
§ 3.
Abstract Galois Theory
....................275
§ 4.
Abstract Valuation Theory
...................284
§ 5.
The Reciprocity Map
.....................290
§ 6.
The General Reciprocity Law
.................299
§ 7.
The
Herbrand
Quotient
....................310
Chapter V: Local Class Field Theory
...............317
§ 1.
The Local Reciprocity Law
..................317
§ 2.
The Norm Residue Symbol over Qp
..............327
§ 3.
The Hubert Symbol
......................333
§ 4.
Formal Groups
........................341
§ 5.
Generalized Cyclotomic Theory
................346
§ 6.
Higher Ramification Groups
..................352
Chapter VI: Global Class Field Theory
..............357
§ 1.
Ideies
and
Idèle
Classes
....................357
§ 2.
Ideies
in Field Extensions
...................368
§ 3.
The
Herbrand
Quotient of the
Idèle
Class Group
.........373
§ 4.
The Class Field Axiom
....................380
§ 5.
The Global Reciprocity Law
..................385
§ 6.
Global Class Fields
......................395
§ 7.
The Ideal-Theoretic Version of Class Field Theory
........405
§ 8.
The Reciprocity Law of the Power Residues
...........414
Chapter
VII: Zeta
Functions and i-series
............419
§ 1.
The Riemann
Zeta
Function
..................419
§ 2.
Dirichlet L-series
.......................434
§ 3.
Theta Series
..........................443
§ 4.
The Higher-dimensional Gamma Function
...........453
Table
of Contents
xvii
§ 5.
The Dedekind
Zeta
Function
..................457
§ 6. Hecke
Characters
...........■............470
§ 7.
Theta Series of Algebraic Number Fields
............484
§ 8. Hecke
L-series
........................493
§ 9.
Values of Dirichlet L-series at Integer Points
..........504
§ 10. Artin
L-series
........................517
§ 11.
The
Artin
Conductor
.....................527
§ 12.
The Functional Equation of
Artin
L-series
...........535
§ 13.
Density Theorems
......................542
Bibliography
...........................551
Index
...............................559
|
| any_adam_object | 1 |
| author | Neukirch, Jürgen 1937-1997 |
| author_GND | (DE-588)117716839 |
| author_facet | Neukirch, Jürgen 1937-1997 |
| author_role | aut |
| author_sort | Neukirch, Jürgen 1937-1997 |
| author_variant | j n jn |
| building | Verbundindex |
| bvnumber | BV012507778 |
| classification_rvk | SK 180 |
| classification_tum | MAT 120f |
| ctrlnum | (OCoLC)439950524 (DE-599)BVBBV012507778 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012507778 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:28:47Z |
| institution | BVB |
| isbn | 3540653996 9783540653998 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008489690 |
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| physical | xvii, 571 Seiten |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Neukirch, Jürgen 1937-1997 (DE-588)117716839 aut Algebraische Zahlentheorie Algebraic number theory Jürgen Neukirch. Transl. from the German by Norbert Schappacher Berlin [u.a.] Springer 1999 xvii, 571 Seiten txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 322 Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf Algebraischer Zahlkörper (DE-588)4068537-8 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 s 1\p DE-604 Algebraischer Zahlkörper (DE-588)4068537-8 s 2\p DE-604 Grundlehren der mathematischen Wissenschaften 322 (DE-604)BV000000395 322 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008489690&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 | Neukirch, Jürgen 1937-1997 Algebraic number theory Grundlehren der mathematischen Wissenschaften Algebraische Zahlentheorie (DE-588)4001170-7 gnd Algebraischer Zahlkörper (DE-588)4068537-8 gnd |
| subject_GND | (DE-588)4001170-7 (DE-588)4068537-8 |
| title | Algebraic number theory |
| title_alt | Algebraische Zahlentheorie |
| title_auth | Algebraic number theory |
| title_exact_search | Algebraic number theory |
| title_full | Algebraic number theory Jürgen Neukirch. Transl. from the German by Norbert Schappacher |
| title_fullStr | Algebraic number theory Jürgen Neukirch. Transl. from the German by Norbert Schappacher |
| title_full_unstemmed | Algebraic number theory Jürgen Neukirch. Transl. from the German by Norbert Schappacher |
| title_short | Algebraic number theory |
| title_sort | algebraic number theory |
| topic | Algebraische Zahlentheorie (DE-588)4001170-7 gnd Algebraischer Zahlkörper (DE-588)4068537-8 gnd |
| topic_facet | Algebraische Zahlentheorie Algebraischer Zahlkörper |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008489690&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT neukirchjurgen algebraischezahlentheorie AT neukirchjurgen algebraicnumbertheory |