The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Commentarii Mathematici Helvetici


Full-Text PDF (584 KB) | Metadata | Table of Contents | CMH summary
Volume 86, Issue 4, 2011, pp. 867–945
DOI: 10.4171/CMH/243

Published online: 2011-09-22

Heegner points and p-adic L-functions for elliptic curves over certain totally real fields

Chung Pang Mok[1]

(1) McMaster University, Hamilton, Canada

For an elliptic curve $E$ over $\mathbb{Q}$ satisfying suitable hypotheses, Bertolini and Darmon have derived a formula for the Heegner point on $E$ in terms of the central derivative of the two variable $p$-adic $L$-function associated to $E$. In this paper, we generalize their work to the setting of totally real fields in which $p$ is inert. We also use this generalization to improve the results obtained by Bertolini–Darmon in the case of an elliptic curve defined over the field of rational numbers.

Keywords: Hilbert modular forms, p-adic L-functions, Heegner points

Mok Chung Pang: Heegner points and p-adic L-functions for elliptic curves over certain totally real fields. Comment. Math. Helv. 86 (2011), 867-945. doi: 10.4171/CMH/243