Local Fields:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1979
|
| Schriftenreihe: | Graduate Texts in Mathematics
67 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., complete for a discrete valuation) fields with finite residue field. For example, such fields are obtained by completing an algebraic number field; that is one of the aspects of "localisation". The chapters are grouped in "parts". There are three preliminary parts: the first two on the general theory of local fields, the third on group coho mology. Local class field theory, strictly speaking, does not appear until the fourth part. Here is a more precise outline of the contents of these four parts: The first contains basic definitions and results on discrete valuation rings, Dedekind domains (which are their "globalisation") and the completion process. The prerequisite for this part is a knowledge of elementary notions of algebra and topology, which may be found for instance in Bourbaki. The second part is concerned with ramification phenomena (different, discriminant, ramification groups, Artin representation). Just as in the first part, no assumptions are made here about the residue fields. It is in this setting that the "norm" map is studied; I have expressed the results in terms of "additive polynomials" and of "multiplicative polynomials", since using the language of algebraic geometry would have led me too far astray |
| Beschreibung: | 1 Online-Ressource (VIII, 245 p) |
| ISBN: | 9781475756739 9781475756753 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4757-5673-9 |
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| 500 | |a The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., complete for a discrete valuation) fields with finite residue field. For example, such fields are obtained by completing an algebraic number field; that is one of the aspects of "localisation". The chapters are grouped in "parts". There are three preliminary parts: the first two on the general theory of local fields, the third on group coho mology. Local class field theory, strictly speaking, does not appear until the fourth part. Here is a more precise outline of the contents of these four parts: The first contains basic definitions and results on discrete valuation rings, Dedekind domains (which are their "globalisation") and the completion process. The prerequisite for this part is a knowledge of elementary notions of algebra and topology, which may be found for instance in Bourbaki. The second part is concerned with ramification phenomena (different, discriminant, ramification groups, Artin representation). Just as in the first part, no assumptions are made here about the residue fields. It is in this setting that the "norm" map is studied; I have expressed the results in terms of "additive polynomials" and of "multiplicative polynomials", since using the language of algebraic geometry would have led me too far astray | ||
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Datensatz im Suchindex
| _version_ | 1804153094982860800 |
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| any_adam_object | |
| author | Serre, Jean-Pierre |
| author_facet | Serre, Jean-Pierre |
| author_role | aut |
| author_sort | Serre, Jean-Pierre |
| author_variant | j p s jps |
| building | Verbundindex |
| bvnumber | BV042421672 |
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| dewey-full | 512 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-5673-9 |
| format | Electronic eBook |
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| id | DE-604.BV042421672 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:09Z |
| institution | BVB |
| isbn | 9781475756739 9781475756753 |
| issn | 0072-5285 |
| language | English |
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| publishDate | 1979 |
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| spelling | Serre, Jean-Pierre Verfasser aut Local Fields by Jean-Pierre Serre New York, NY Springer New York 1979 1 Online-Ressource (VIII, 245 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 67 0072-5285 The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., complete for a discrete valuation) fields with finite residue field. For example, such fields are obtained by completing an algebraic number field; that is one of the aspects of "localisation". The chapters are grouped in "parts". There are three preliminary parts: the first two on the general theory of local fields, the third on group coho mology. Local class field theory, strictly speaking, does not appear until the fourth part. Here is a more precise outline of the contents of these four parts: The first contains basic definitions and results on discrete valuation rings, Dedekind domains (which are their "globalisation") and the completion process. The prerequisite for this part is a knowledge of elementary notions of algebra and topology, which may be found for instance in Bourbaki. The second part is concerned with ramification phenomena (different, discriminant, ramification groups, Artin representation). Just as in the first part, no assumptions are made here about the residue fields. It is in this setting that the "norm" map is studied; I have expressed the results in terms of "additive polynomials" and of "multiplicative polynomials", since using the language of algebraic geometry would have led me too far astray Mathematics Algebra Mathematik Lokaler Körper (DE-588)4266744-6 gnd rswk-swf Lokale Klassenkörpertheorie (DE-588)4168107-1 gnd rswk-swf Lokale Klasse (DE-588)4577640-4 gnd rswk-swf Homologietheorie (DE-588)4141714-8 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Körpertheorie (DE-588)4164455-4 gnd rswk-swf Klassenkörpertheorie (DE-588)4030951-4 gnd rswk-swf Kohomologie (DE-588)4031700-6 gnd rswk-swf Körpertheorie (DE-588)4164455-4 s Lokale Klasse (DE-588)4577640-4 s 1\p DE-604 Lokale Klassenkörpertheorie (DE-588)4168107-1 s Kohomologie (DE-588)4031700-6 s 2\p DE-604 Lokaler Körper (DE-588)4266744-6 s 3\p DE-604 Kommutative Algebra (DE-588)4164821-3 s 4\p DE-604 Homologietheorie (DE-588)4141714-8 s 5\p DE-604 Klassenkörpertheorie (DE-588)4030951-4 s 6\p DE-604 https://doi.org/10.1007/978-1-4757-5673-9 Verlag Volltext 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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Serre, Jean-Pierre Local Fields Mathematics Algebra Mathematik Lokaler Körper (DE-588)4266744-6 gnd Lokale Klassenkörpertheorie (DE-588)4168107-1 gnd Lokale Klasse (DE-588)4577640-4 gnd Homologietheorie (DE-588)4141714-8 gnd Kommutative Algebra (DE-588)4164821-3 gnd Körpertheorie (DE-588)4164455-4 gnd Klassenkörpertheorie (DE-588)4030951-4 gnd Kohomologie (DE-588)4031700-6 gnd |
| subject_GND | (DE-588)4266744-6 (DE-588)4168107-1 (DE-588)4577640-4 (DE-588)4141714-8 (DE-588)4164821-3 (DE-588)4164455-4 (DE-588)4030951-4 (DE-588)4031700-6 |
| title | Local Fields |
| title_auth | Local Fields |
| title_exact_search | Local Fields |
| title_full | Local Fields by Jean-Pierre Serre |
| title_fullStr | Local Fields by Jean-Pierre Serre |
| title_full_unstemmed | Local Fields by Jean-Pierre Serre |
| title_short | Local Fields |
| title_sort | local fields |
| topic | Mathematics Algebra Mathematik Lokaler Körper (DE-588)4266744-6 gnd Lokale Klassenkörpertheorie (DE-588)4168107-1 gnd Lokale Klasse (DE-588)4577640-4 gnd Homologietheorie (DE-588)4141714-8 gnd Kommutative Algebra (DE-588)4164821-3 gnd Körpertheorie (DE-588)4164455-4 gnd Klassenkörpertheorie (DE-588)4030951-4 gnd Kohomologie (DE-588)4031700-6 gnd |
| topic_facet | Mathematics Algebra Mathematik Lokaler Körper Lokale Klassenkörpertheorie Lokale Klasse Homologietheorie Kommutative Algebra Körpertheorie Klassenkörpertheorie Kohomologie |
| url | https://doi.org/10.1007/978-1-4757-5673-9 |
| work_keys_str_mv | AT serrejeanpierre localfields |