The Euler system of generalized Heegner cycles

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...

DIAGONAL CYCLES AND EULER SYSTEMS I: A p-ADIC GROSS-ZAGIER FORMULA

This article is the first in a series devoted to studying generalised Gross-KudlaSchoen diagonal cycles in the product of three Kuga-Sato varieties and the Euler system properties of the associated Selmer classes, with special emphasis on their application to the Birch–Swinnerton-Dyer conjecture and the theory of Stark-Heegner points. The basis for the entire study is a p-adic formula of Gross-...

The Euler System of Heegner Points

Equidistribution of Heegner Points and Ternary Quadratic Forms

We prove new equidistribution results for Galois orbits of Heegner points with respect to reduction maps at inert primes. The arguments are based on two different techniques: primitive representations of integers by quadratic forms and distribution relations for Heegner points. Our results generalize one of the equidistribution theorems established by Cornut and Vatsal in the sense that we allo...

Algebraic cycles and Stark-Heegner points

Introduction Stark-Heegner points are canonical global points on elliptic curves or modular abelian varieties which admit–often conjecturally–explicit analytic constructions as well as direct relations to L-series, both complex and p-adic. The ultimate aim of these notes is to present a new approach to this theory based on algebraic cycles, Rankin triple product L-functions, and p-adic families...