Tame Representations of Local Weil Groups and of Chain Groups of Local Principal Orders:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1986
|
| Schriftenreihe: | Sitzungsberichte der Heidelberger Akademie der Wissenschaften, Mathematisch-naturwissenschaftliche Klasse
1986,3 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | We begin by making clear the meaning of the term "tame". The higher ramification groups, on the one hand, and the one-units of chain groups, on the other, are to lie in the kernels of the respective representations considered. We shall establish a very natural and very well behaved relationship between representations of the two groups mentioned in the title, with all the right properties, and in particular functorial under base change and essentially preserving root numbers. All this will be done in full generality for all principal orders. The formal setup for this also throws new light on the nature of Gauss sums and in particular leads to a canonical closed formula for tame Galois Gauss sums. In many ways the "tame" and the "wild" theory have distinct features and distinct points of interest. The "wild" theory is much harder and - as far as it goes at present - technically rather complicated. On the "tame" side, once we have developed a number of new ideas, we get a complete comprehensive theory, from which technical difficulties have disappeared, and which has a naturality, and perhaps elegance, which seems rather rare in this gen,eral area. Among the principal new concepts we are introducing are those of "similarity" of representations in both contexts and that of the Galois algebra of a principal order. One might expect that this Galois algebra will also be of importance in the wild situation |
| Beschreibung: | 1 Online-Ressource (100p) |
| ISBN: | 9783642465949 9783540173403 |
| ISSN: | 0371-0165 |
| DOI: | 10.1007/978-3-642-46594-9 |
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Datensatz im Suchindex
| _version_ | 1804153097081061376 |
|---|---|
| any_adam_object | |
| author | Fröhlich, Albrecht |
| author_facet | Fröhlich, Albrecht |
| author_role | aut |
| author_sort | Fröhlich, Albrecht |
| author_variant | a f af |
| building | Verbundindex |
| bvnumber | BV042422518 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863946152 (DE-599)BVBBV042422518 |
| dewey-full | 512.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7 |
| dewey-search | 512.7 |
| dewey-sort | 3512.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-46594-9 |
| format | Electronic eBook |
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| id | DE-604.BV042422518 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:11Z |
| institution | BVB |
| isbn | 9783642465949 9783540173403 |
| issn | 0371-0165 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857935 |
| oclc_num | 863946152 |
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| publishDate | 1986 |
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| publisher | Springer Berlin Heidelberg |
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| series | Sitzungsberichte der Heidelberger Akademie der Wissenschaften, Mathematisch-naturwissenschaftliche Klasse |
| series2 | Sitzungsberichte der Heidelberger Akademie der Wissenschaften, Mathematisch-naturwissenschaftliche Klasse |
| spelling | Fröhlich, Albrecht Verfasser aut Tame Representations of Local Weil Groups and of Chain Groups of Local Principal Orders by Albrecht Fröhlich Berlin, Heidelberg Springer Berlin Heidelberg 1986 1 Online-Ressource (100p) txt rdacontent c rdamedia cr rdacarrier Sitzungsberichte der Heidelberger Akademie der Wissenschaften, Mathematisch-naturwissenschaftliche Klasse 1986 / 3 0371-0165 We begin by making clear the meaning of the term "tame". The higher ramification groups, on the one hand, and the one-units of chain groups, on the other, are to lie in the kernels of the respective representations considered. We shall establish a very natural and very well behaved relationship between representations of the two groups mentioned in the title, with all the right properties, and in particular functorial under base change and essentially preserving root numbers. All this will be done in full generality for all principal orders. The formal setup for this also throws new light on the nature of Gauss sums and in particular leads to a canonical closed formula for tame Galois Gauss sums. In many ways the "tame" and the "wild" theory have distinct features and distinct points of interest. The "wild" theory is much harder and - as far as it goes at present - technically rather complicated. On the "tame" side, once we have developed a number of new ideas, we get a complete comprehensive theory, from which technical difficulties have disappeared, and which has a naturality, and perhaps elegance, which seems rather rare in this gen,eral area. Among the principal new concepts we are introducing are those of "similarity" of representations in both contexts and that of the Galois algebra of a principal order. One might expect that this Galois algebra will also be of importance in the wild situation Mathematics Number theory Number Theory Mathematik Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Weil-Gruppe (DE-588)4140074-4 gnd rswk-swf Kettengruppe (DE-588)4140070-7 gnd rswk-swf Weil-Gruppe (DE-588)4140074-4 s Darstellungstheorie (DE-588)4148816-7 s 1\p DE-604 Kettengruppe (DE-588)4140070-7 s 2\p DE-604 Sitzungsberichte der Heidelberger Akademie der Wissenschaften, Mathematisch-naturwissenschaftliche Klasse 1986,3 (DE-604)BV002535862 1986,3 https://doi.org/10.1007/978-3-642-46594-9 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 |
| spellingShingle | Fröhlich, Albrecht Tame Representations of Local Weil Groups and of Chain Groups of Local Principal Orders Sitzungsberichte der Heidelberger Akademie der Wissenschaften, Mathematisch-naturwissenschaftliche Klasse Mathematics Number theory Number Theory Mathematik Darstellungstheorie (DE-588)4148816-7 gnd Weil-Gruppe (DE-588)4140074-4 gnd Kettengruppe (DE-588)4140070-7 gnd |
| subject_GND | (DE-588)4148816-7 (DE-588)4140074-4 (DE-588)4140070-7 |
| title | Tame Representations of Local Weil Groups and of Chain Groups of Local Principal Orders |
| title_auth | Tame Representations of Local Weil Groups and of Chain Groups of Local Principal Orders |
| title_exact_search | Tame Representations of Local Weil Groups and of Chain Groups of Local Principal Orders |
| title_full | Tame Representations of Local Weil Groups and of Chain Groups of Local Principal Orders by Albrecht Fröhlich |
| title_fullStr | Tame Representations of Local Weil Groups and of Chain Groups of Local Principal Orders by Albrecht Fröhlich |
| title_full_unstemmed | Tame Representations of Local Weil Groups and of Chain Groups of Local Principal Orders by Albrecht Fröhlich |
| title_short | Tame Representations of Local Weil Groups and of Chain Groups of Local Principal Orders |
| title_sort | tame representations of local weil groups and of chain groups of local principal orders |
| topic | Mathematics Number theory Number Theory Mathematik Darstellungstheorie (DE-588)4148816-7 gnd Weil-Gruppe (DE-588)4140074-4 gnd Kettengruppe (DE-588)4140070-7 gnd |
| topic_facet | Mathematics Number theory Number Theory Mathematik Darstellungstheorie Weil-Gruppe Kettengruppe |
| url | https://doi.org/10.1007/978-3-642-46594-9 |
| volume_link | (DE-604)BV002535862 |
| work_keys_str_mv | AT frohlichalbrecht tamerepresentationsoflocalweilgroupsandofchaingroupsoflocalprincipalorders |