Simple algebras, base change, and the advanced theory of the trace formula:
A general principle, discovered by Robert Langlands and named by him the "functoriality principle," predicts relations between automorphic forms on arithmetic subgroups of different reductive groups. Langlands functoriality relates the eigenvalues of Hecke operators acting on the automorph...
Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[1989]
|
| Schriftenreihe: | Annals of Mathematics Studies
number 120 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | A general principle, discovered by Robert Langlands and named by him the "functoriality principle," predicts relations between automorphic forms on arithmetic subgroups of different reductive groups. Langlands functoriality relates the eigenvalues of Hecke operators acting on the automorphic forms on two groups (or the local factors of the "automorphic representations" generated by them). In the few instances where such relations have been probed, they have led to deep arithmetic consequences. This book studies one of the simplest general problems in the theory, that of relating automorphic forms on arithmetic subgroups of GL(n,E) and GL(n,F) when E/F is a cyclic extension of number fields. (This is known as the base change problem for GL(n).) The problem is attacked and solved by means of the trace formula. The book relies on deep and technical results obtained by several authors during the last twenty years. It could not serve as an introduction to them, but, by giving complete references to the published literature, the authors have made the work useful to a reader who does not know all the aspects of the theory of automorphic forms |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed May 30, 2016) |
| Beschreibung: | 1 online resource |
| ISBN: | 9781400882403 9780691085180 |
| DOI: | 10.1515/9781400882403 |
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| 520 | |a A general principle, discovered by Robert Langlands and named by him the "functoriality principle," predicts relations between automorphic forms on arithmetic subgroups of different reductive groups. Langlands functoriality relates the eigenvalues of Hecke operators acting on the automorphic forms on two groups (or the local factors of the "automorphic representations" generated by them). In the few instances where such relations have been probed, they have led to deep arithmetic consequences. This book studies one of the simplest general problems in the theory, that of relating automorphic forms on arithmetic subgroups of GL(n,E) and GL(n,F) when E/F is a cyclic extension of number fields. (This is known as the base change problem for GL(n).) The problem is attacked and solved by means of the trace formula. The book relies on deep and technical results obtained by several authors during the last twenty years. It could not serve as an introduction to them, but, by giving complete references to the published literature, the authors have made the work useful to a reader who does not know all the aspects of the theory of automorphic forms | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Arthur, James 1944- Clozel, Laurent 1953- |
| author_GND | (DE-588)133218317 (DE-588)1133380344 |
| author_facet | Arthur, James 1944- Clozel, Laurent 1953- |
| author_role | aut aut |
| author_sort | Arthur, James 1944- |
| author_variant | j a ja l c lc |
| building | Verbundindex |
| bvnumber | BV043712500 |
| classification_rvk | SI 830 SK 240 SK 260 |
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| ctrlnum | (ZDB-23-DGG)9781400882403 (OCoLC)1165518049 (DE-599)BVBBV043712500 |
| dewey-full | 512/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.2 |
| dewey-search | 512/.2 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400882403 |
| format | Electronic eBook |
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| id | DE-604.BV043712500 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:33:08Z |
| institution | BVB |
| isbn | 9781400882403 9780691085180 |
| language | English |
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| psigel | ZDB-23-DGG ZDB-23-PST |
| publishDate | 1989 |
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| publisher | Princeton University Press |
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| series | Annals of Mathematics Studies |
| series2 | Annals of Mathematics Studies |
| spelling | Arthur, James 1944- (DE-588)133218317 aut Simple algebras, base change, and the advanced theory of the trace formula Laurent Clozel, James Arthur Princeton, NJ Princeton University Press [1989] © 1989 1 online resource txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 120 Description based on online resource; title from PDF title page (publisher's Web site, viewed May 30, 2016) A general principle, discovered by Robert Langlands and named by him the "functoriality principle," predicts relations between automorphic forms on arithmetic subgroups of different reductive groups. Langlands functoriality relates the eigenvalues of Hecke operators acting on the automorphic forms on two groups (or the local factors of the "automorphic representations" generated by them). In the few instances where such relations have been probed, they have led to deep arithmetic consequences. This book studies one of the simplest general problems in the theory, that of relating automorphic forms on arithmetic subgroups of GL(n,E) and GL(n,F) when E/F is a cyclic extension of number fields. (This is known as the base change problem for GL(n).) The problem is attacked and solved by means of the trace formula. The book relies on deep and technical results obtained by several authors during the last twenty years. It could not serve as an introduction to them, but, by giving complete references to the published literature, the authors have made the work useful to a reader who does not know all the aspects of the theory of automorphic forms In English Automorphic forms Representations of groups Trace formulas Spur (DE-588)4056591-9 gnd rswk-swf Spurformel (DE-588)4182612-7 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Automorphe Form (DE-588)4003972-9 gnd rswk-swf Spur Mathematik (DE-588)4202272-1 gnd rswk-swf Automorphe Form (DE-588)4003972-9 s Spurformel (DE-588)4182612-7 s Gruppentheorie (DE-588)4072157-7 s 1\p DE-604 Darstellungstheorie (DE-588)4148816-7 s 2\p DE-604 3\p DE-604 Spur Mathematik (DE-588)4202272-1 s 4\p DE-604 Spur (DE-588)4056591-9 s 5\p DE-604 Clozel, Laurent 1953- (DE-588)1133380344 aut Erscheint auch als Druck-Ausgabe 978-0-691-08518-0 Annals of Mathematics Studies number 120 (DE-604)BV040389493 120 https://doi.org/10.1515/9781400882403?locatt=mode:legacy Verlag URL des Erstveröffentlichers 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 |
| spellingShingle | Arthur, James 1944- Clozel, Laurent 1953- Simple algebras, base change, and the advanced theory of the trace formula Annals of Mathematics Studies Automorphic forms Representations of groups Trace formulas Spur (DE-588)4056591-9 gnd Spurformel (DE-588)4182612-7 gnd Gruppentheorie (DE-588)4072157-7 gnd Darstellungstheorie (DE-588)4148816-7 gnd Automorphe Form (DE-588)4003972-9 gnd Spur Mathematik (DE-588)4202272-1 gnd |
| subject_GND | (DE-588)4056591-9 (DE-588)4182612-7 (DE-588)4072157-7 (DE-588)4148816-7 (DE-588)4003972-9 (DE-588)4202272-1 |
| title | Simple algebras, base change, and the advanced theory of the trace formula |
| title_auth | Simple algebras, base change, and the advanced theory of the trace formula |
| title_exact_search | Simple algebras, base change, and the advanced theory of the trace formula |
| title_full | Simple algebras, base change, and the advanced theory of the trace formula Laurent Clozel, James Arthur |
| title_fullStr | Simple algebras, base change, and the advanced theory of the trace formula Laurent Clozel, James Arthur |
| title_full_unstemmed | Simple algebras, base change, and the advanced theory of the trace formula Laurent Clozel, James Arthur |
| title_short | Simple algebras, base change, and the advanced theory of the trace formula |
| title_sort | simple algebras base change and the advanced theory of the trace formula |
| topic | Automorphic forms Representations of groups Trace formulas Spur (DE-588)4056591-9 gnd Spurformel (DE-588)4182612-7 gnd Gruppentheorie (DE-588)4072157-7 gnd Darstellungstheorie (DE-588)4148816-7 gnd Automorphe Form (DE-588)4003972-9 gnd Spur Mathematik (DE-588)4202272-1 gnd |
| topic_facet | Automorphic forms Representations of groups Trace formulas Spur Spurformel Gruppentheorie Darstellungstheorie Automorphe Form Spur Mathematik |
| url | https://doi.org/10.1515/9781400882403?locatt=mode:legacy |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT arthurjames simplealgebrasbasechangeandtheadvancedtheoryofthetraceformula AT clozellaurent simplealgebrasbasechangeandtheadvancedtheoryofthetraceformula |