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AuthorBrown, Martin L. author
TitleHeegner Modules and Elliptic Curves [electronic resource] / by Martin L. Brown
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 2004
Connect tohttp://dx.doi.org/10.1007/b98488
Descript X, 518 p. online resource

SUMMARY

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

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


Mathematics Algebraic geometry Number theory Mathematics Number Theory Algebraic Geometry



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