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SUMMARY:Euler systems and the Birch--Swinnerton-Dyer conjecture - Sarah Ze
 rbes (University College London)
DTSTART:20150210T161500Z
DTEND:20150210T171500Z
UID:TALK56681@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:I show how Beilinson's Eisenstein symbol can be used to constr
 uct motivic cohomology classes attached to pairs of modular forms of weigh
 t >= 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 correspond
 ing Rankin-Selberg L-function. This is joint work with Kings and Loeffler\
 , extending my previous work with Lei and Loeffler for weight 2 forms. Thi
 s Euler system has several arithmetic applications\, including one divisib
 ility in the Iwasawa main conjecture for modular forms over imaginary quad
 ratic fields\, and cases of the finiteness of Tate--Shafarevich groups for
  elliptic curves twisted by dihedral Artin representations. 
LOCATION:MR13
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