Class Field Theory: From Theory to Practice
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2003
|
| Schriftenreihe: | Springer Monographs in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Global class field theory is a major achievement of algebraic number theory, based on the functorial properties of the reciprocity map and the existence theorem. The author works out the consequences and the practical use of these results by giving detailed studies and illustrations of classical subjects (classes, idèles, ray class fields, symbols, reciprocity laws, Hasse's principles, the Grunwald-Wang theorem, Hilbert's towers,...). He also proves some new or less-known results (reflection theorem, structure of the abelian closure of a number field) and lays emphasis on the invariant (/cal T) p, of abelian p-ramification, which is related to important Galois cohomology properties and p-adic conjectures. This book, intermediary between the classical literature published in the sixties and the recent computational literature, gives much material in an elementary way, and is suitable for students, researchers, and all who are fascinated by this theory. In the corrected 2nd printing 2005, the author improves some mathematical and bibliographical details and adds a few pages about rank computations for the general reflection theorem; then he gives an arithmetical interpretation for usual class groups, and applies this to the Spiegelungssatz for quadratic fields and for the p-th cyclotomic field regarding the Kummer--Vandiver conjecture in a probabilistic point of view |
| Beschreibung: | 1 Online-Ressource (XIII, 491 p) |
| ISBN: | 9783662113233 9783642079085 |
| ISSN: | 1439-7382 |
| DOI: | 10.1007/978-3-662-11323-3 |
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| dewey-ones | 512 - Algebra |
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| discipline | Mathematik |
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| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662113233 9783642079085 |
| issn | 1439-7382 |
| language | English |
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| spelling | Gras, Georges Verfasser aut Class Field Theory From Theory to Practice by Georges Gras Berlin, Heidelberg Springer Berlin Heidelberg 2003 1 Online-Ressource (XIII, 491 p) txt rdacontent c rdamedia cr rdacarrier Springer Monographs in Mathematics 1439-7382 Global class field theory is a major achievement of algebraic number theory, based on the functorial properties of the reciprocity map and the existence theorem. The author works out the consequences and the practical use of these results by giving detailed studies and illustrations of classical subjects (classes, idèles, ray class fields, symbols, reciprocity laws, Hasse's principles, the Grunwald-Wang theorem, Hilbert's towers,...). He also proves some new or less-known results (reflection theorem, structure of the abelian closure of a number field) and lays emphasis on the invariant (/cal T) p, of abelian p-ramification, which is related to important Galois cohomology properties and p-adic conjectures. This book, intermediary between the classical literature published in the sixties and the recent computational literature, gives much material in an elementary way, and is suitable for students, researchers, and all who are fascinated by this theory. In the corrected 2nd printing 2005, the author improves some mathematical and bibliographical details and adds a few pages about rank computations for the general reflection theorem; then he gives an arithmetical interpretation for usual class groups, and applies this to the Spiegelungssatz for quadratic fields and for the p-th cyclotomic field regarding the Kummer--Vandiver conjecture in a probabilistic point of view Mathematics Number theory Number Theory Mathematik Klassenkörpertheorie (DE-588)4030951-4 gnd rswk-swf Klassenkörpertheorie (DE-588)4030951-4 s 1\p DE-604 https://doi.org/10.1007/978-3-662-11323-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gras, Georges Class Field Theory From Theory to Practice Mathematics Number theory Number Theory Mathematik Klassenkörpertheorie (DE-588)4030951-4 gnd |
| subject_GND | (DE-588)4030951-4 |
| title | Class Field Theory From Theory to Practice |
| title_auth | Class Field Theory From Theory to Practice |
| title_exact_search | Class Field Theory From Theory to Practice |
| title_full | Class Field Theory From Theory to Practice by Georges Gras |
| title_fullStr | Class Field Theory From Theory to Practice by Georges Gras |
| title_full_unstemmed | Class Field Theory From Theory to Practice by Georges Gras |
| title_short | Class Field Theory |
| title_sort | class field theory from theory to practice |
| title_sub | From Theory to Practice |
| topic | Mathematics Number theory Number Theory Mathematik Klassenkörpertheorie (DE-588)4030951-4 gnd |
| topic_facet | Mathematics Number theory Number Theory Mathematik Klassenkörpertheorie |
| url | https://doi.org/10.1007/978-3-662-11323-3 |
| work_keys_str_mv | AT grasgeorges classfieldtheoryfromtheorytopractice |