Heegner Modules and Elliptic Curves
Springer Berlin (Verlag)
978-3-540-22290-3 (ISBN)
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.
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.
| Erscheint lt. Verlag | 15.7.2004 |
|---|---|
| Reihe/Serie | Lecture Notes in Mathematics |
| Zusatzinfo | X, 518 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 780 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Schlagworte | 11F52, 11G05, 11G09, 11G15, 11G40, 11R58, • 14F20, 14G10, 14H52, 14J27, 14K22 • Drinfeld Modules • Elliptic Curves • Elliptische Kurven • finite field • Heegner Points • Tate Conjecture • Tate-Shafarevich Groups |
| ISBN-10 | 3-540-22290-1 / 3540222901 |
| ISBN-13 | 978-3-540-22290-3 / 9783540222903 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
aus dem Bereich
