Heegner Points on Cartan Non-split Curves
Canadian journal of mathematics, Tome 68 (2016) no. 2, pp. 422-444
Voir la notice de l'article provenant de la source Cambridge
Let $E/\mathbb{Q}$ be an elliptic curve of conductor $N$ , and let $K$ be an imaginary quadratic field such that the root number of $E/K$ is −1. Let $O$ be an order in $K$ and assume that there exists an odd prime $p$ such that ${{p}^{2}}\,\parallel \,N$ , and $p$ is inert in $O$ . Although there are no Heegner points on ${{X}_{0}}(N)$ attached to $O$ , in this article we construct such points on Cartan non-split curves. In order to do that, we give a method to compute Fourier expansions for forms on Cartan non-split curves, and prove that the constructed points form a Heegner system as in the classical case.
Kohen, Daniel; Pacetti, Ariel. Heegner Points on Cartan Non-split Curves. Canadian journal of mathematics, Tome 68 (2016) no. 2, pp. 422-444. doi: 10.4153/CJM-2015-047-6
@article{10_4153_CJM_2015_047_6,
author = {Kohen, Daniel and Pacetti, Ariel},
title = {Heegner {Points} on {Cartan} {Non-split} {Curves}},
journal = {Canadian journal of mathematics},
pages = {422--444},
year = {2016},
volume = {68},
number = {2},
doi = {10.4153/CJM-2015-047-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-047-6/}
}
TY - JOUR AU - Kohen, Daniel AU - Pacetti, Ariel TI - Heegner Points on Cartan Non-split Curves JO - Canadian journal of mathematics PY - 2016 SP - 422 EP - 444 VL - 68 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-047-6/ DO - 10.4153/CJM-2015-047-6 ID - 10_4153_CJM_2015_047_6 ER -
Cité par Sources :