Class Field Theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1986
|
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
280 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Class field theory, which is so immediately compelling in its main assertions, has, ever since its invention, suffered from the fact that its proofs have required a complicated and, by comparison with the results, rather imperspicuous system of arguments which have tended to jump around all over the place. My earlier presentation of the theory [41] has strengthened me in the belief that a highly elaborate mechanism, such as, for example, cohomology, might not be adequate for a number-theoretical law admitting a very direct formulation, and that the truth of such a law must be susceptible to a far more immediate insight. I was determined to write the present, new account of class field theory by the discovery that, in fact, both the local and the global reciprocity laws may be subsumed under a purely grouptheoretical principle, admitting an entirely elementary description. This description makes possible a new foundation for the entire theory. The rapid advance to the main theorems of class field theory which results from this approach has made it possible to include in this volume the most important consequences and elaborations, and further related theories, with the exception of the cohomology version which I have this time excluded. This remains a significant variant, rich in application, but its principal results should be directly obtained from the material treated here |
| Beschreibung: | 1 Online-Ressource (VIII, 142 p) |
| ISBN: | 9783642824654 9783642824678 |
| DOI: | 10.1007/978-3-642-82465-4 |
Internformat
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| 490 | 1 | |a Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |v 280 | |
| 500 | |a Class field theory, which is so immediately compelling in its main assertions, has, ever since its invention, suffered from the fact that its proofs have required a complicated and, by comparison with the results, rather imperspicuous system of arguments which have tended to jump around all over the place. My earlier presentation of the theory [41] has strengthened me in the belief that a highly elaborate mechanism, such as, for example, cohomology, might not be adequate for a number-theoretical law admitting a very direct formulation, and that the truth of such a law must be susceptible to a far more immediate insight. I was determined to write the present, new account of class field theory by the discovery that, in fact, both the local and the global reciprocity laws may be subsumed under a purely grouptheoretical principle, admitting an entirely elementary description. This description makes possible a new foundation for the entire theory. The rapid advance to the main theorems of class field theory which results from this approach has made it possible to include in this volume the most important consequences and elaborations, and further related theories, with the exception of the cohomology version which I have this time excluded. This remains a significant variant, rich in application, but its principal results should be directly obtained from the material treated here | ||
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Datensatz im Suchindex
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| author | Neukirch, Jürgen 1937-1997 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-82465-4 |
| format | Electronic eBook |
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| id | DE-604.BV042423039 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T06:38:47Z |
| institution | BVB |
| isbn | 9783642824654 9783642824678 |
| language | English |
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| series | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |
| series2 | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |
| spelling | Neukirch, Jürgen 1937-1997 Verfasser (DE-588)117716839 aut Class Field Theory by Jürgen Neukirch Berlin, Heidelberg Springer Berlin Heidelberg 1986 1 Online-Ressource (VIII, 142 p) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 280 Class field theory, which is so immediately compelling in its main assertions, has, ever since its invention, suffered from the fact that its proofs have required a complicated and, by comparison with the results, rather imperspicuous system of arguments which have tended to jump around all over the place. My earlier presentation of the theory [41] has strengthened me in the belief that a highly elaborate mechanism, such as, for example, cohomology, might not be adequate for a number-theoretical law admitting a very direct formulation, and that the truth of such a law must be susceptible to a far more immediate insight. I was determined to write the present, new account of class field theory by the discovery that, in fact, both the local and the global reciprocity laws may be subsumed under a purely grouptheoretical principle, admitting an entirely elementary description. This description makes possible a new foundation for the entire theory. The rapid advance to the main theorems of class field theory which results from this approach has made it possible to include in this volume the most important consequences and elaborations, and further related theories, with the exception of the cohomology version which I have this time excluded. This remains a significant variant, rich in application, but its principal results should be directly obtained from the material treated here Mathematics Number theory Number Theory Mathematik Klassenkörpertheorie (DE-588)4030951-4 gnd rswk-swf Klassenkörpertheorie (DE-588)4030951-4 s 1\p DE-604 Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 280 (DE-604)BV049758308 280 https://doi.org/10.1007/978-3-642-82465-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Neukirch, Jürgen 1937-1997 Class Field Theory Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics Mathematics Number theory Number Theory Mathematik Klassenkörpertheorie (DE-588)4030951-4 gnd |
| subject_GND | (DE-588)4030951-4 |
| title | Class Field Theory |
| title_auth | Class Field Theory |
| title_exact_search | Class Field Theory |
| title_full | Class Field Theory by Jürgen Neukirch |
| title_fullStr | Class Field Theory by Jürgen Neukirch |
| title_full_unstemmed | Class Field Theory by Jürgen Neukirch |
| title_short | Class Field Theory |
| title_sort | class field theory |
| 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/10.1007/978-3-642-82465-4 |
| volume_link | (DE-604)BV049758308 |
| work_keys_str_mv | AT neukirchjurgen classfieldtheory |