Math @ Duke

Publications [#338521] of Samit Dasgupta
Papers Published
 Dasgupta, S, StarkHeegner points on modular Jacobians,
Annales Scientifiques De L’École Normale Supérieure, vol. 38 no. 3
(May, 2005),
pp. 427469, Societe Mathematique de France [doi]
(last updated on 2022/01/25)
Abstract: We present a construction which lifts Darmon's StarkHeegner 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)pnew of the Jacobian of X0(Np). This theorem generalizes a conjecture of Mazur, Tate, and Teitelbaum on the padic periods of elliptic curves, which was proven by Greenberg and Stevens. As a byproduct of our theorem, we obtain an efficient method of calculating the padic periods of J0(Np)pnew. © 2005 Elsevier SAS. All rights reserved.


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