On the p-Adic Birch, Swinnerton–Dyer Conjecture for Non-semistable Reduction
نویسندگان
چکیده
منابع مشابه
ON RUBIN’S VARIANT OF THE p-ADIC BIRCH AND SWINNERTON-DYER CONJECTURE
We study Rubin’s variant of the p-adic Birch and Swinnerton-Dyer conjecture for CM elliptic curves concerning certain special values of the Katz two-variable p-adic L-function that lie outside the range of p-adic interpolation.
متن کاملON RUBIN’S VARIANT OF THE p-ADIC BIRCH AND SWINNERTON-DYER CONJECTURE II
Let E/Q be an elliptic curve with complex multiplication by the ring of integers of an imaginary quadratic field K. In 1991, by studying a certain special value of the Katz two-variable p-adic L-function lying outside the range of p-adic interpolation, K. Rubin formulated a p-adic variant of the Birch and Swinnerton-Dyer conjecture when E(K) is infinite, and he proved that his conjecture is tru...
متن کاملA 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 descri...
متن کاملON THE BIRATIONAL p-ADIC SECTION CONJECTURE
In this manuscript we introduce/prove a Z/p meta-abelian form of the birational p-adic Section Conjecture for curves. This is a much stronger result than the usual p-adic birational Section Conjecture for curves, and makes an effective p-adic Section Conjecture for curves quite plausible.
متن کاملp-adic height pairings on abelian varieties with semistable ordinary reduction
We prove that for abelian varieties with semistable ordinary reduction the p-adic Mazur-Tate height pairing is induced by the unit root splitting of the Hodge filtration on the first deRham cohomology.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2002
ISSN: 0022-314X
DOI: 10.1006/jnth.2001.2755