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＜E-Book＞
Heegner Modules and Elliptic Curves / by Martin L. Brown
(Lecture Notes in Mathematics. ISSN:16179692 ; 1849)

Edition	1st ed. 2004.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	2004
Size	X, 518 p : online resource
Authors	*Brown, Martin L author SpringerLink (Online service)
Subjects	LCSH:Number theory LCSH:Algebraic geometry FREE:Number Theory FREE:Algebraic Geometry
Notes	Preface -- Introduction -- Preliminaries -- Bruhat-Tits trees with complex multiplication -- Heegner sheaves -- The Heegner module -- Cohomology of the Heegner module -- Finiteness of the Tate-Shafarevich groups -- Appendix A.: Rigid analytic modular forms -- Appendix B.: Automorphic forms and elliptic curves over function fields -- References -- Index 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 HTTP:URL=https://doi.org/10.1007/b98488

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