Advanced analytic number theory: 1 Ramification theoretic methods
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
1983
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| Series: | Contemporary mathematics
... |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 190 S |
| ISBN: | 0821850156 |
Staff View
MARC
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| 245 | 1 | 0 | |a Advanced analytic number theory |n 1 |p Ramification theoretic methods |c Carlos Jiménez Moreno |
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Record in the Search Index
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| adam_text | CONTENTS
Preface
Chapter 0. Introduction _ 1
§1. A historical perspective
§2. The explicit formulas: motivation
Chapter I. Galois Theory for Infinite Extensions 25
§1. Fundamental Theorem of Galois Theory for infinite extensions
§2. Topological properties of Gal(K /K)
§ 3. Example
Chapter II. Protective Limits 31
§1. Basic definitions
§2. Examples
§ 3. Homomo rph i sms
Chapter III. Elementary Theory of l adia Integration 45
§1. Distributions and measures
§2. Measures on groups
§ 3. Riemann sums
§A. 5, adic Haar measures
§5. Examples
Chapter IV. Ramification Theory 55
§1. The v function
§2. Transitivity properties of the v function
§3. The different
§4. Transitivity properties of the different
§5. Complementary basis
§6. Fundamental inequality and the C invariant
§7. Quotients of Galois groups and Herbrand s Theorem
Chapter V. Multiplicative versus Additive Reduction 79
§1. The case of a local field
§2. The module structure of the unit group
§3. The case of an elliptic curve
vi CONTENTS
Chapter VI. Ramification of Abelian Extensions 95
§1. Index computations
§2. Main Theorem
Chapter VII. The Weil Groups of a Local Field 109
§1. The Frobenius automorphism
§2. The relative Weil group of a non archimedean local field
§3. The absolute Weil group
54. The Weil group of an archimedean local field
§5. The Weil Deligne group
Appendix: The non abelian local reciprocity law
Chapter VIII. Shafarevitch s Theorem 133
§1. Representations of a simple algebra
§2. Factor sets
§3. Subalgebras of central simple algebras
§4. Cyclic algebras
§5. Algebras and group extensions
§6. Powers of central simple algebras
§7. Generators of the Brauer group
§8. Structure of the relative Weil group
§9. Shafarevitch s Theorem
Appendix: I. The Brauer group of central simple algebras over K
II. The group H2(G,KX)
Chapter IX. The Herbrand Distribution 157
§1. The Herbrand distribution: definition and basic facts
§2. The support of the Herbrand distribution
§3. Determination of the Herbrand distribution on Gal(K /K)
§4. Functoriality properties of the Herbrand distribution
§5. The Herbrand distribution and measures on the Weil group
§6. The integral formula for the Herbrand distribution
§7. Conductors, the Artin representation, and the Herbrand distribution
Bibliography 185
Index I89
|
| adam_txt |
CONTENTS
Preface
Chapter 0. Introduction _ 1
§1. A historical perspective
§2. The explicit formulas: motivation
Chapter I. Galois Theory for Infinite Extensions 25
§1. Fundamental Theorem of Galois Theory for infinite extensions
§2. Topological properties of Gal(K'/K)
§ 3. Example
Chapter II. Protective Limits 31
§1. Basic definitions
§2. Examples
§ 3. Homomo rph i sms
Chapter III. Elementary Theory of l adia Integration 45
§1. Distributions and measures
§2. Measures on groups
§ 3. Riemann sums
§A. 5, adic Haar measures
§5. Examples
Chapter IV. Ramification Theory 55
§1. The v function
§2. Transitivity properties of the v function
§3. The different
§4. Transitivity properties of the different
§5. Complementary basis
§6. Fundamental inequality and the C invariant
§7. Quotients of Galois groups and Herbrand's Theorem
Chapter V. Multiplicative versus Additive Reduction 79
§1. The case of a local field
§2. The module structure of the unit group
§3. The case of an elliptic curve
vi CONTENTS
Chapter VI. Ramification of Abelian Extensions 95
§1. Index computations
§2. Main Theorem
Chapter VII. The Weil Groups of a Local Field 109
§1. The Frobenius automorphism
§2. The relative Weil group of a non archimedean local field
§3. The absolute Weil group
54. The Weil group of an archimedean local field
§5. The Weil Deligne group
Appendix: The non abelian local reciprocity law
Chapter VIII. Shafarevitch's Theorem 133
§1. Representations of a simple algebra
§2. Factor sets
§3. Subalgebras of central simple algebras
§4. Cyclic algebras
§5. Algebras and group extensions
§6. Powers of central simple algebras
§7. Generators of the Brauer group
§8. Structure of the relative Weil group
§9. Shafarevitch's Theorem
Appendix: I. The Brauer group of central simple algebras over K
II. The group H2(G,KX)
Chapter IX. The Herbrand Distribution 157
§1. The Herbrand distribution: definition and basic facts
§2. The support of the Herbrand distribution
§3. Determination of the Herbrand distribution on Gal(K /K)
§4. Functoriality properties of the Herbrand distribution
§5. The Herbrand distribution and measures on the Weil group
§6. The integral formula for the Herbrand distribution
§7. Conductors, the Artin representation, and the Herbrand distribution
Bibliography 185
Index I89 |
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| publisher | American Math. Soc. |
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| series | Contemporary mathematics |
| series2 | Contemporary mathematics |
| spelling | Jiménez Moreno, Carlos Verfasser aut Advanced analytic number theory 1 Ramification theoretic methods Carlos Jiménez Moreno Providence, RI American Math. Soc. 1983 VIII, 190 S txt rdacontent n rdamedia nc rdacarrier Contemporary mathematics ... Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Algebraischer Körper (DE-588)4141852-9 gnd rswk-swf Analytische Zahlentheorie (DE-588)4001870-2 gnd rswk-swf Analytische Zahlentheorie (DE-588)4001870-2 s DE-604 Algebraischer Körper (DE-588)4141852-9 s Zahlentheorie (DE-588)4067277-3 s (DE-604)BV021844162 1 Contemporary mathematics ... (DE-604)BV000003365 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015219119&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jiménez Moreno, Carlos Advanced analytic number theory Contemporary mathematics Zahlentheorie (DE-588)4067277-3 gnd Algebraischer Körper (DE-588)4141852-9 gnd Analytische Zahlentheorie (DE-588)4001870-2 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4141852-9 (DE-588)4001870-2 |
| title | Advanced analytic number theory |
| title_auth | Advanced analytic number theory |
| title_exact_search | Advanced analytic number theory |
| title_exact_search_txtP | Advanced analytic number theory |
| title_full | Advanced analytic number theory 1 Ramification theoretic methods Carlos Jiménez Moreno |
| title_fullStr | Advanced analytic number theory 1 Ramification theoretic methods Carlos Jiménez Moreno |
| title_full_unstemmed | Advanced analytic number theory 1 Ramification theoretic methods Carlos Jiménez Moreno |
| title_short | Advanced analytic number theory |
| title_sort | advanced analytic number theory ramification theoretic methods |
| topic | Zahlentheorie (DE-588)4067277-3 gnd Algebraischer Körper (DE-588)4141852-9 gnd Analytische Zahlentheorie (DE-588)4001870-2 gnd |
| topic_facet | Zahlentheorie Algebraischer Körper Analytische Zahlentheorie |
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