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Euler System

Automorphic forms, Shimura varieties, Galois representations and L-functions December 01, 2014 - December 05, 2014

December 04, 2014 (02:00 PM PST - 03:00 PM PST)
Speaker(s): Sarah Zerbes (ETH Zürich)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC



I show how Beilinson's Eisenstein symbol give rise to 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. 

22431?type=thumb Notes Zerbes 311 KB application/pdf Download
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