Heegner Modules and Elliptic Curves

• Main Author: Brown, Martin L. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004.
• Edition: 1st ed. 2004.
• Series: Lecture Notes in Mathematics, 1849
• Subjects: Number theory.; Algebraic geometry.; Number Theory.; Algebraic Geometry.
• Physical Description: X, 518 p. online resource.
• ISBN: 9783540444756
• ISSN: 0075-8434 ;
• DOI: 10.1007/b98488

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.