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

Abstract:

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 p-adic L-function of a modular abelian variety and showing that it satisfies the appropriate interpolation property. This relies on a careful normalization of the p-adic L-function, which we achieve by a comparison of pe...

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Publication date:
2012-10-09
URN:
uuid:fb003887-47c0-4a60-a04a-47bc88219a19
Source identifiers:
398264
Local pid:
pubs:398264

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