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Mathematics - Number Theory and Discrete Mathematics | Heegner Modules and Elliptic Curves

Heegner Modules and Elliptic Curves

Series: Lecture Notes in Mathematics, Vol. 1849

Brown, Martin L.

2004, X, 518 p.

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  • About this book

Heegner points on both modular curves and elliptic curves over global fields of any characteristic form 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 conjecture is equivalent to the Birch and Swinnerton-Dyer conjecture for the corresponding elliptic curves over global fields.

Content Level » Research

Keywords » Drinfeld Modules - Elliptic Curves - Heegner Points - Tate Conjecture - Tate-Shafarevich Groups - finite field

Related subjects » Algebra - Number Theory and Discrete Mathematics

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