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Tate Classes and Endoscopy for GSp4

组织者

刁晗生 , 杜衡 , 胡悦科 , Bin Xu , Yihang Zhu

演讲者

Naomi Sweeting

时间

2024年11月25日 10:00 至 11:00

地点

Online

线上

Zoom 455 260 1552 (YMSC)

摘要

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.