Geodesic
p–adic Families of Cohomological Modular Forms for Indefinite Quaternion Algebras and the Jacquet–LanglandsCorrespondence
Canadian journal of mathematics, Tome 68 (2016) no. 5, pp. 961-998

Voir la notice de l'article provenant de la source Cambridge

DOI

We use the method of Ash and Stevens to prove the existence of small slope $p$ -adic families of cohomological modular forms for an indefinite quaternion algebra $B$ . We prove that the Jacquet–Langlands correspondence relating modular forms on $\text{G}{{\text{L}}_{\text{2}}}/\mathbb{Q}$ and cohomomological modular forms for $B$ is compatible with the formation of $p$ -adic families. This result is an analogue of a theorem of Chenevier concerning definite quaternion algebras.
DOI : 10.4153/CJM-2015-062-x
Mots-clés : 11F11, 11F67, 11F85, modular forms, p–adic families, Jacquet–Langlands correspondence, Shimura curves, eigencurves 
Greenberg, Matthew; Seveso, Marco. p–adic Families of Cohomological Modular Forms for Indefinite Quaternion Algebras and the Jacquet–LanglandsCorrespondence. Canadian journal of mathematics, Tome 68 (2016) no. 5, pp. 961-998. doi: 10.4153/CJM-2015-062-x
@article{10_4153_CJM_2015_062_x,
     author = {Greenberg, Matthew and Seveso, Marco},
     title = {p{\textendash}adic {Families} of {Cohomological} {Modular} {Forms} for {Indefinite} {Quaternion} {Algebras} and the {Jacquet{\textendash}LanglandsCorrespondence}},
     journal = {Canadian journal of mathematics},
     pages = {961--998},
     year = {2016},
     volume = {68},
     number = {5},
     doi = {10.4153/CJM-2015-062-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-062-x/}
}
TY  - JOUR
AU  - Greenberg, Matthew
AU  - Seveso, Marco
TI  - p–adic Families of Cohomological Modular Forms for Indefinite Quaternion Algebras and the Jacquet–LanglandsCorrespondence
JO  - Canadian journal of mathematics
PY  - 2016
SP  - 961
EP  - 998
VL  - 68
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-062-x/
DO  - 10.4153/CJM-2015-062-x
ID  - 10_4153_CJM_2015_062_x
ER  - 
%0 Journal Article
%A Greenberg, Matthew
%A Seveso, Marco
%T p–adic Families of Cohomological Modular Forms for Indefinite Quaternion Algebras and the Jacquet–LanglandsCorrespondence
%J Canadian journal of mathematics
%D 2016
%P 961-998
%V 68
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-062-x/
%R 10.4153/CJM-2015-062-x
%F 10_4153_CJM_2015_062_x

Cité par Sources :