Congruences between modular forms modulo prime powers
Given a prime p ≥ 5 and an abstract odd representation pn with coefficients modulo pn (for some n ≥ 1) and big image, we prove the existence of a lift of pn to characteristic 0 whenever local lifts exist (under minor technical conditions). Moreover, our results allow to chose the lift's inertia...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_16089057_v_n6_p1609_Camporino |
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todo:paper_16089057_v_n6_p1609_Camporino2023-10-03T16:27:52Z Congruences between modular forms modulo prime powers Camporino, M. Pacetti, A. Galois representations Modular forms Given a prime p ≥ 5 and an abstract odd representation pn with coefficients modulo pn (for some n ≥ 1) and big image, we prove the existence of a lift of pn to characteristic 0 whenever local lifts exist (under minor technical conditions). Moreover, our results allow to chose the lift's inertial type at all primes but finitely many (where the lift is of Steinberg type). We apply this result to the realm of modular forms, proving a level lowering theorem modulo prime powers and providing examples of level raising. An easy application of our main result proves that given a modular eigenform f whose Galois representation is not induced from a character (i.e., f has no inner twists), for all primes p but finitely many, and for all positive integers n, there exists an eigenform g = f, which is congruent to f modulo pn. © European Mathematical Society. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_16089057_v_n6_p1609_Camporino |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Galois representations Modular forms |
| spellingShingle |
Galois representations Modular forms Camporino, M. Pacetti, A. Congruences between modular forms modulo prime powers |
| topic_facet |
Galois representations Modular forms |
| description |
Given a prime p ≥ 5 and an abstract odd representation pn with coefficients modulo pn (for some n ≥ 1) and big image, we prove the existence of a lift of pn to characteristic 0 whenever local lifts exist (under minor technical conditions). Moreover, our results allow to chose the lift's inertial type at all primes but finitely many (where the lift is of Steinberg type). We apply this result to the realm of modular forms, proving a level lowering theorem modulo prime powers and providing examples of level raising. An easy application of our main result proves that given a modular eigenform f whose Galois representation is not induced from a character (i.e., f has no inner twists), for all primes p but finitely many, and for all positive integers n, there exists an eigenform g = f, which is congruent to f modulo pn. © European Mathematical Society. |
| format |
JOUR |
| author |
Camporino, M. Pacetti, A. |
| author_facet |
Camporino, M. Pacetti, A. |
| author_sort |
Camporino, M. |
| title |
Congruences between modular forms modulo prime powers |
| title_short |
Congruences between modular forms modulo prime powers |
| title_full |
Congruences between modular forms modulo prime powers |
| title_fullStr |
Congruences between modular forms modulo prime powers |
| title_full_unstemmed |
Congruences between modular forms modulo prime powers |
| title_sort |
congruences between modular forms modulo prime powers |
| url |
http://hdl.handle.net/20.500.12110/paper_16089057_v_n6_p1609_Camporino |
| work_keys_str_mv |
AT camporinom congruencesbetweenmodularformsmoduloprimepowers AT pacettia congruencesbetweenmodularformsmoduloprimepowers |
| _version_ |
1807314793304948736 |