Heegner Modules and Elliptic Curves - 1849

Heegner points on both modular curves and elliptic curves over global fields of any characteristicform the topic of this research monograph.

The Heegner module of an elliptic curve is an original concept introduced in this text.

The computation of the cohomology of the Heegner module is the main technical result and is applied to prove the Tate conjecture for a class of elliptic surfaces over finite fields, this conjectureis equivalent to the Birch and Swinnerton-Dyer conjecture for the corresponding elliptic curves over global fields.