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
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/88143
Acceder
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spelling 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 Técnicas2025-09-29T10:34:09Zoai: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:34982025-09-29 10:34:10.185CONICET 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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score 13.069144

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