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SUMMARY:Fernando Trejos Suarez (Princeton)
DTSTART:20261117T210000Z
DTEND:20261117T220000Z
DTSTAMP:20261112T133733Z
UID:MITNT/148
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/148/">
 Euler Systems and Bloch--Kato for the Triple Product</a>\nby Fernando Trej
 os Suarez (Princeton) as part of MIT number theory seminar\n\nLecture held
  in Room 2-449 in the Simons Building (building 2).\n\nAbstract\nWe discus
 s the construction of an Euler system for the triple product\, the p-adic 
 Galois representation V = V_1 x V_2 x V_3\, where V_1\,V_2\,V_3 are the 2-
 dimensional representations attached to cuspforms f_1\,f_2\,f_3. Applicati
 ons include new cases of the Bloch—Kato conjecture: e.g. in the case tha
 t f_i is an elliptic curve E_i over the rationals\, and if χ denotes a no
 n-trivial Dirichlet character\, we prove (under some technical assumptions
 ) that the non-vanishing of L(E_1 x E_2 x E_3 x χ\, s) at the central val
 ue s=2 implies the vanishing of the relevant Selmer group for V(χ). The c
 onstruction is geometric\, taking place on the Shimura variety for GSp(4)\
 , and uses the pullback method pioneered by Sangiovanni—Skinner. (This t
 alk will not assume any prior knowledge of Euler systems.)\n
LOCATION:https://researchseminars.org/talk/MITNT/148/
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