no. 1
Number theory
Base change for elliptic curves over real quadratic fields
[Changement de base pour les courbes elliptiques sur les corps quadratiques réels]
Présenté par : Jean-Pierre Serre
Dieulefait, Luis1 ; Freitas, Nuno1
1 Mathematisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany
Comptes Rendus. Mathématique, Tome 353 (2015) no. 1, pp. 1-4

Let E be an elliptic curve over a real quadratic field K and F/K a totally real finite Galois extension. We prove that E/F is modular.

Soit E une courbe elliptique sur un corps quadratique réel K et F/K une extension totalement réele, finie et galoisienne. On demontre que E/F est modulaire.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.10.006

Dieulefait, Luis 1 ; Freitas, Nuno 1

1 Mathematisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany 
@article{CRMATH_2015__353_1_1_0,
     author = {Dieulefait, Luis and Freitas, Nuno},
     title = {Base change for elliptic curves over real quadratic fields},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1--4},
     year = {2015},
     publisher = {Elsevier},
     volume = {353},
     number = {1},
     doi = {10.1016/j.crma.2014.10.006},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.crma.2014.10.006/}
}
TY  - JOUR
AU  - Dieulefait, Luis
AU  - Freitas, Nuno
TI  - Base change for elliptic curves over real quadratic fields
JO  - Comptes Rendus. Mathématique
PY  - 2015
SP  - 1
EP  - 4
VL  - 353
IS  - 1
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.crma.2014.10.006/
DO  - 10.1016/j.crma.2014.10.006
LA  - en
ID  - CRMATH_2015__353_1_1_0
ER  - 
%0 Journal Article
%A Dieulefait, Luis
%A Freitas, Nuno
%T Base change for elliptic curves over real quadratic fields
%J Comptes Rendus. Mathématique
%D 2015
%P 1-4
%V 353
%N 1
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.crma.2014.10.006/
%R 10.1016/j.crma.2014.10.006
%G en
%F CRMATH_2015__353_1_1_0
Dieulefait, Luis; Freitas, Nuno. Base change for elliptic curves over real quadratic fields. Comptes Rendus. Mathématique, Tome 353 (2015) no. 1, pp. 1-4. doi: 10.1016/j.crma.2014.10.006

[1] Dieulefait, L. Langlands base change for GL(2), Ann. Math., Volume 176 (2012), pp. 1015-1038

[2] Dieulefait, L. Automorphy of Symm5(GL(2)) and base change (with Appendix A by R. Guralnick and Appendix B by L. Dieulefait and T. Gee) (submitted for publication) | arXiv

[3] Freitas, N.; Le Hung, B.V.; Siksek, S. Elliptic curves over real quadratic fields are modular, Invent. Math. (2014) (in press) | DOI

[4] Guitart, X.; Rotger, V.; Zhao, Y. Almost totally complex points on elliptic curves, Trans. Amer. Math. Soc., Volume 336 (2014), pp. 2773-2802

[5] Jacquet, H.; Langlands, R.P. Automorphic Forms on GL(2), Lect. Notes Math., vol. 114, Springer-Verlag, Berlin, 1970

[6] Langlands, R.P. Base Change for GL(2), Ann. Math. Stud., vol. 96, 1980

Cité par Sources :