Heegner Modules and Elliptic Curves

• Κύριος συγγραφέας: Brown, Martin L. (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004.
• Έκδοση: 1st ed. 2004.
• Σειρά: Lecture Notes in Mathematics, 1849
• Θέματα: Number theory.; Algebraic geometry.; Number Theory.; Algebraic Geometry.
• Φυσική περιγραφή: 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.