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On rigid analytic uniformizations of Jacobians of Shimura curves
Longo, Matteo; Rotger, Víctor; Vigni, Stefano
Centre de Recerca Matemàtica
The main goal of this article is to give an explicit rigid analytic uniformization of the maximal toric quotient of the Jacobian of a Shimura curve over Q at a prime dividing exactly the level. This result can be viewed as complementary to the classical theorem of Cerednik and Drinfeld which provides rigid analytic uniformizations at primes dividing the discriminant. As a corollary, we offer a proof of a conjecture formulated by M. Greenberg in hispaper on Stark-Heegner points and quaternionic Shimura curves, thus making Greenberg's construction of local points on elliptic curves over Q unconditional.
2010-02
514 - Geometria
Corbes
Integració de funcions
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Prepublicacions del Centre de Recerca Matemàtica;932
         

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