Publications [#338521] of Samit Dasgupta

Papers Published

1. Dasgupta, S, Stark-Heegner points on modular Jacobians, Annales Scientifiques de l'Ecole Normale Superieure, vol. 38 no. 3 (May, 2005), pp. 427-469, Societe Mathematique de France [doi]
   (last updated on 2025/05/12)

   Abstract:
   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.