Stark-Heegner points on modular Jacobians

Published

Journal Article

We present a construction which lifts Darmon's Stark-Heegner points from elliptic curves to certain modular Jacobians. Let N be a positive integer and let p be a prime not dividing N. Our essential idea is to replace the modular symbol attached to an elliptic curve E of conductor Np with the universal modular symbol for Γ0(Np). We then construct a certain torus T over Qp and lattice L ⊂ T, and prove that the quotient T/L is isogenous to the maximal toric quotient J0(Np)p-new of the Jacobian of X0(Np). This theorem generalizes a conjecture of Mazur, Tate, and Teitelbaum on the p-adic periods of elliptic curves, which was proven by Greenberg and Stevens. As a by-product of our theorem, we obtain an efficient method of calculating the p-adic periods of J0(Np)p-new. © 2005 Elsevier SAS. All rights reserved.

Full Text

Duke Authors

Cited Authors

  • Dasgupta, S

Published Date

  • May 1, 2005

Published In

Volume / Issue

  • 38 / 3

Start / End Page

  • 427 - 469

International Standard Serial Number (ISSN)

  • 0012-9593

Digital Object Identifier (DOI)

  • 10.1016/j.ansens.2005.03.002

Citation Source

  • Scopus