Tate Classes and Endoscopy for GSp4

BIMSA-YMSC Tsinghua Number Theory Seminar

Organizers：

Hansheng Diao, Heng Du, Yueke Hu, Bin Xu, Yihang Zhu

Speaker：

Naomi Sweeting (Princeton)

Time：

Mon., 10:00-11:00 am, Nov. 25, 2024

Online：

Zoom Meeting ID: 4552601552

Passcode: YMSC

Title：

Tate Classes and Endoscopy for GSp4

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.

About the speaker：

I am a number theorist interested in the Bloch-Kato conjectures, automorphic forms, and special cycles on Shimura varieties. I am currently an NSF postdoc of Chris Skinner. Before that, I was a student of Mark Kisin at Harvard. Starting in Fall 2026, I will be an Assistant Professor at MIT.