Brown, M. L.

Heegner modules and elliptic curves / M. [Martin] L. Brown. - Berlin ; New York : Springer, ©2004. - 1 online resource (x, 517 pages) - Lecture notes in mathematics, 1849 0075-8434 ; . - Lecture notes in mathematics (Springer-Verlag) ; 1849. .

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.


9783540444756 3540444750

10.1007/b98488 doi

Curves, Elliptic.
Algebraic fields.
Homology theory.
Algebraic fields.
Curves, Elliptic.
Homology theory.
Algebraïsche meetkunde.
Curvas eliticas.
Geometria algébrica.

Electronic books.

QA3 QA567.2.E44 / .L28 no. 1849

510 s 516.3/52

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