Tate Classes and Endoscopy for GSp4
Organizers
Hansheng Diao
, Heng Du
, Yueke Hu
, Bin Xu
, Yihang Zhu
Speaker
Naomi Sweeting
Time
Monday, November 25, 2024 10:00 AM - 11:00 AM
Venue
Online
Online
Zoom 455 260 1552
(YMSC)
Abstract
Weissauer proved using the theory of endoscopy 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 natural to ask whether one can construct algebraic cycles giving rise to these 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 endoscopic L-packets on GSp4. In the non-generic case, one can at least show that all the Tate classes arise from Hodge cycles. I will explain these results and their proofs, which rely on the theta correspondence.