Heegner Modules and Elliptic Curves

• Main Author: Brown, Martin L. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004.
• Edition: 1st ed. 2004.
• Series: Lecture Notes in Mathematics, 1849
• Subjects: Number theory.; Algebraic geometry.; Number Theory.; Algebraic Geometry.

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 te...

Table of 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.