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SUMMARY:Waqar Shah (UCSB)
DTSTART:20221006T233000Z
DTEND:20221007T010000Z
DTSTAMP:20260423T024622Z
UID:UCSBsga/39
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSBsga/39/"
 >Zeta elements for Shimura varieties II: Examples</a>\nby Waqar Shah (UCSB
 ) as part of UCSB Seminar on Geometry and Arithmetic\n\n\nAbstract\nIn thi
 s second talk\, I will begin by reviewing a generalization of the double c
 oset decomposition recipe for parahoric subgroups originally due to Lansky
  and illustrate the recipe in some simple cases. Paired with the machinery
  of zeta elements and mixed Hecke correspondences that I described in my p
 revious talk\, this decomposition recipe yields a powerful and effective m
 ethod for studying norm relation problems for classes constructed using th
 e push-forward formalism that would otherwise be too cumbersome to study d
 irectly. I will illustrate this method in two key situations of arithmetic
  interest that were recently studied using alternate methods: Shimura vari
 eties of GU(1\,2n-1) & GSp_4. I will also highlight several key technical 
 advantages of this approach over the earlier ones in these cases. Time per
 mitting\, I will discuss a new example of an Euler system for the Galois r
 epresentations arising from GU(2\,2) Shimura varieties.\n
LOCATION:https://researchseminars.org/talk/UCSBsga/39/
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