Heegner issues on either modular curves and elliptic curves over worldwide fields of any characteristic form the subject of this learn monograph. The Heegner module of an elliptic curve is an unique notion brought during this textual content. The computation of the cohomology of the Heegner module is the most technical outcome and is utilized to end up the Tate conjecture for a category of elliptic surfaces over finite fields, this conjecture is such as the Birch and Swinnerton-Dyer conjecture for the corresponding elliptic curves over worldwide fields.
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