Explicit Approaches to Elliptic Curves and Modular Abelian Varieties

Award Number: DMS-1161226

Program Solicitation

William Stein


The projects in this proposal would generalize the highly influential tables of Cremona to the next totally real number field and to higher dimensional modular abelian varieties. This would improve on algorithms available for computing with elliptic curves and abelian varieties, and provide useful data and tools for number theory researchers. The proposed research would also advance techniques for constructing points and cohomology classes on elliptic curves, and for understanding the arithmetic of elliptic curves over number fields. This project would have as a concrete deliverable new publicly available tables and software that will be of use to many number theorists.

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