Congruences between modular forms modulo prime powers
- Autores
- Camporino, Maximiliano Javier; Pacetti, Ariel Martín
- Año de publicación
- 2018
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Given a prime p≥5 and an abstract odd representation ρ n with coefficients modulo p n (for some n≥1 and big image, we prove the existence of a lift of ρ n 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.
Fil: Camporino, Maximiliano Javier. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Pacetti, Ariel Martín. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina - Materia
-
Modular Forms
Galois Representations - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/88143
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Congruences between modular forms modulo prime powersCamporino, Maximiliano JavierPacetti, Ariel MartínModular FormsGalois Representationshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Given a prime p≥5 and an abstract odd representation ρ n with coefficients modulo p n (for some n≥1 and big image, we prove the existence of a lift of ρ n 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.Fil: Camporino, Maximiliano Javier. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Pacetti, Ariel Martín. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaUniversidad Autónoma de Madrid2018-12-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/88143Camporino, Maximiliano Javier; Pacetti, Ariel Martín; Congruences between modular forms modulo prime powers; Universidad Autónoma de Madrid; Revista Matematica Iberoamericana; 34; 4; 6-12-2018; 1609-16430213-2230CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1312.4925info:eu-repo/semantics/altIdentifier/doi/10.4171/rmi/1037info:eu-repo/semantics/altIdentifier/url/https://dialnet.unirioja.es/servlet/articulo?codigo=6791254info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:07:39Zoai:ri.conicet.gov.ar:11336/88143instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:07:39.347CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Congruences between modular forms modulo prime powers |
title |
Congruences between modular forms modulo prime powers |
spellingShingle |
Congruences between modular forms modulo prime powers Camporino, Maximiliano Javier Modular Forms Galois Representations |
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 |
dc.creator.none.fl_str_mv |
Camporino, Maximiliano Javier Pacetti, Ariel Martín |
author |
Camporino, Maximiliano Javier |
author_facet |
Camporino, Maximiliano Javier Pacetti, Ariel Martín |
author_role |
author |
author2 |
Pacetti, Ariel Martín |
author2_role |
author |
dc.subject.none.fl_str_mv |
Modular Forms Galois Representations |
topic |
Modular Forms Galois Representations |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
Given a prime p≥5 and an abstract odd representation ρ n with coefficients modulo p n (for some n≥1 and big image, we prove the existence of a lift of ρ n 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. Fil: Camporino, Maximiliano Javier. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina Fil: Pacetti, Ariel Martín. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina |
description |
Given a prime p≥5 and an abstract odd representation ρ n with coefficients modulo p n (for some n≥1 and big image, we prove the existence of a lift of ρ n 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. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-12-06 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/88143 Camporino, Maximiliano Javier; Pacetti, Ariel Martín; Congruences between modular forms modulo prime powers; Universidad Autónoma de Madrid; Revista Matematica Iberoamericana; 34; 4; 6-12-2018; 1609-1643 0213-2230 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/88143 |
identifier_str_mv |
Camporino, Maximiliano Javier; Pacetti, Ariel Martín; Congruences between modular forms modulo prime powers; Universidad Autónoma de Madrid; Revista Matematica Iberoamericana; 34; 4; 6-12-2018; 1609-1643 0213-2230 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1312.4925 info:eu-repo/semantics/altIdentifier/doi/10.4171/rmi/1037 info:eu-repo/semantics/altIdentifier/url/https://dialnet.unirioja.es/servlet/articulo?codigo=6791254 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Universidad Autónoma de Madrid |
publisher.none.fl_str_mv |
Universidad Autónoma de Madrid |
dc.source.none.fl_str_mv |
reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
reponame_str |
CONICET Digital (CONICET) |
collection |
CONICET Digital (CONICET) |
instname_str |
Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.name.fl_str_mv |
CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.mail.fl_str_mv |
dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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13.13397 |