Heegner modules and elliptic curves / M. [Martin] L. Brown.

By: Brown, M. L. (Martin L.)
Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag): 1849.Publisher: Berlin ; New York : Springer, ©2004Description: 1 online resource (x, 517 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9783540444756; 3540444750Subject(s): Curves, Elliptic | Algebraic fields | Homology theory | Algebraic fields | Curves, Elliptic | Homology theory | Algebraïsche meetkunde | Getaltheorie | Curvas eliticas | Geometria algébricaGenre/Form: Electronic books. Additional physical formats: Print version:: Heegner modules and elliptic curves.DDC classification: 510 s | 516.3/52 LOC classification: QA3 | .L28 no. 1849 | QA567.2.E44Online resources: Click here to access online
Contents:
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.
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.
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Includes bibliographical references (pages 507-510) and index.

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.

English.

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