منابع مشابه
Efficient Computation of P-adic Heights
We analyse and drastically improve the running time of the algorithm of Mazur, Stein and Tate for computing the canonical cyclotomic p-adic height of a point on an elliptic curve E/Q, where E has good ordinary reduction at p ≥ 5.
متن کاملComputation of p-Adic Heights and Log Convergence
This paper is about computational questions regarding p-adic height pairings on elliptic curves over a global field K. The main stumbling block to computing them efficiently is in calculating, for each of the completions Kv at the places v of K dividing p, a single quantity: the value of the p-adic modular form E2 associated to the elliptic curve. Thanks to the work of Kedlaya et al., we offer ...
متن کاملDerived p-adic heights
2 Derived p-adic heights 2.1 Derived heights for cyclic groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Comparison of pairings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Compatibility of the derived heights . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4 Derived p-adic heights . . . . . . . . . . . . . . . . . . . . . . . . . ....
متن کاملp-adic heights of Heegner points and Λ-adic regulators
Let E be an elliptic curve defined over Q. The aim of this paper is to make it possible to compute Heegner L-functions and anticyclotomic Λ-adic regulators of E, which were studied by Mazur-Rubin and Howard. We generalize results of Cohen and Watkins and thereby compute Heegner points of nonfundamental discriminant. We then prove a relationship between the denominator of a point of E defined ov...
متن کاملCLASS INVARIANTS AND p-ADIC HEIGHTS
Let F be a number field with ring of integers OF , and let E/OF be an abelian scheme of arbitrary dimension. In this paper, we study the class invariant homomoprhisms on E with respect to powers of a prime p of ordinary reduction of E. Our main result implies that if the p-adic Birch and Swinnerton-Dyer conjecture holds for E, then the kernels of these homomorphisms are of bounded order. It fol...
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ژورنال
عنوان ژورنال: LMS Journal of Computation and Mathematics
سال: 2008
ISSN: 1461-1570
DOI: 10.1112/s1461157000000528