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2016

A p-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties

4 years 3 months ago
A p-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties
Mazur, Tate, and Teitelbaum gave a p-adic analogue of the Birch and Swinnerton-Dyer conjecture for elliptic curves. We provide a generalization of their conjecture in the good ordinary case to higher dimensional modular abelian varieties over the rationals by constructing the padic L-function of a modular abelian variety and showing it satisfies the appropriate interpolation property. We describe the techniques used to formulate the conjecture and give evidence supporting the conjecture in the case when the modular abelian variety is of dimension 2.
Jennifer S. Balakrishnan, J. Steffen Müller,
Added 08 Apr 2016
Updated 08 Apr 2016
Type Journal
Year 2016
Where MOC
Authors Jennifer S. Balakrishnan, J. Steffen Müller, William Stein
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