Euler systems and the Birch--Swinnerton-Dyer conjecture

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• Sarah Zerbes (University College London)
• Tuesday 10 February 2015, 16:15-17:15
• MR13.

If you have a question about this talk, please contact Jack Thorne.

I show how Beilinson’s Eisenstein symbol can be used to construct motivic cohomology classes attached to pairs of modular forms of weight >= 2. These motivic cohomology classes can be used to construct an Euler system—a compatible family of global cohomology classes—attached to pairs of modular forms, related to the critical values of the corresponding Rankin-Selberg L-function. This is joint work with Kings and Loeffler, extending my previous work with Lei and Loeffler for weight 2 forms. This Euler system has several arithmetic applications, including one divisibility in the Iwasawa main conjecture for modular forms over imaginary quadratic fields, and cases of the finiteness of Tate—Shafarevich groups for elliptic curves twisted by dihedral Artin representations.

This talk is part of the Number Theory Seminar series.

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