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SUMMARY:Naomi Sweeting (Harvard)
DTSTART:20230228T210000Z
DTEND:20230228T220000Z
DTSTAMP:20260423T010236Z
UID:UAANTS/57
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UAANTS/57/">
 Tate Classes and Endoscopy for GSp4</a>\nby Naomi Sweeting (Harvard) as pa
 rt of University of Arizona Algebra and Number Theory Seminar\n\nLecture h
 eld in ENR2 S395.\n\nAbstract\nWeissauer proved using the theory of endosc
 opy that the Galois representations associated to classical modular forms 
 of weight two appear in the middle cohomology of both a modular curve and 
 a Siegel modular threefold. Correspondingly\, there are large families of 
 Tate classes on the product of these two Shimura varieties\, and it is nat
 ural to ask whether one can construct algebraic cycles giving rise to thes
 e Tate classes. It turns out that a natural algebraic cycle generates some
 \, but not all\, of the Tate classes: to be precise\, it generates exactly
  the Tate classes which are associated to generic members of the endoscopi
 c L-packets on GSp4. In the non-generic case\, one can at least show that 
 all the Tate classes arise from Hodge cycles. I'll explain these results a
 nd sketch their proofs\, which rely on the theta correspondence.\n
LOCATION:https://researchseminars.org/talk/UAANTS/57/
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