Heegner points, Heegner cycles, and congruences
نویسنده
چکیده
We define certain objects associated to a modular elliptic curve E and a discriminant D satisfying suitable conditions. These objects interpolate special values of the complex L-functions associated to E over the quadratic field Q( √ D), in the same way that Bernouilli numbers interpolate special values of Dirichlet L-series. Following an approach of Mazur and Tate [MT], one can make conjectures about congruences satisfied by these objects which are resonant with the usual Birch and Swinnerton-Dyer conjectures. These conjectures exhibit some surprising features not apparent in the classical case.
منابع مشابه
A refined conjecture of Mazur-Tate type for Heegner points
In [MT1], B. Mazur and J. Tate present a “refined conjecture of Birch and Swinnerton-Dyer type” for a modular elliptic curve E. This conjecture relates congruences for certain integral homology cycles on E(C) (the modular symbols) to the arithmetic of E over Q. In this paper we formulate an analogous conjecture for E over suitable imaginary quadratic fields, in which the role of the modular sym...
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