Potential automorphy over CM fields
Let F be a CM number field. We prove modularity lifting theorems for regular n-dimensional Galois representations over F without any self-duality condition. We deduce that all elliptic curves E over F are potentially modular, and furthermore satisfy the Sato–Tate conjecture. As an application of a d...
| Main Authors: | , , , , , , , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Princeton University Press
2023
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| _version_ | 1797109414591725568 |
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| author | Allen, PB Calegari, F Caraiani, A Gee, T Helm, D Le Hung, BV Newton, J Scholze, P Taylor, R Thorne, JA |
| author_facet | Allen, PB Calegari, F Caraiani, A Gee, T Helm, D Le Hung, BV Newton, J Scholze, P Taylor, R Thorne, JA |
| author_sort | Allen, PB |
| collection | OXFORD |
| description | Let F be a CM number field. We prove modularity lifting theorems for
regular n-dimensional Galois representations over F without any self-duality
condition. We deduce that all elliptic curves E over F are potentially modular, and furthermore satisfy the Sato–Tate conjecture. As an application
of a different sort, we also prove the Ramanujan Conjecture for weight zero
cuspidal automorphic representations for GL2(AF ). |
| first_indexed | 2024-03-07T07:41:36Z |
| format | Journal article |
| id | oxford-uuid:e0921a07-a067-4a43-b717-977fd65ba8c9 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:41:36Z |
| publishDate | 2023 |
| publisher | Princeton University Press |
| record_format | dspace |
| spelling | oxford-uuid:e0921a07-a067-4a43-b717-977fd65ba8c92023-04-20T09:57:17ZPotential automorphy over CM fieldsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e0921a07-a067-4a43-b717-977fd65ba8c9EnglishSymplectic ElementsPrinceton University Press2023Allen, PBCalegari, FCaraiani, AGee, THelm, DLe Hung, BVNewton, JScholze, PTaylor, RThorne, JALet F be a CM number field. We prove modularity lifting theorems for regular n-dimensional Galois representations over F without any self-duality condition. We deduce that all elliptic curves E over F are potentially modular, and furthermore satisfy the Sato–Tate conjecture. As an application of a different sort, we also prove the Ramanujan Conjecture for weight zero cuspidal automorphic representations for GL2(AF ). |
| spellingShingle | Allen, PB Calegari, F Caraiani, A Gee, T Helm, D Le Hung, BV Newton, J Scholze, P Taylor, R Thorne, JA Potential automorphy over CM fields |
| title | Potential automorphy over CM fields |
| title_full | Potential automorphy over CM fields |
| title_fullStr | Potential automorphy over CM fields |
| title_full_unstemmed | Potential automorphy over CM fields |
| title_short | Potential automorphy over CM fields |
| title_sort | potential automorphy over cm fields |
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