Zeta functions of Shimura varieties: past, present, and the near future
By Yihang Zhu
Appears in collection : Automorphic forms, endoscopy and trace formulas / Formes automorphes, endoscopie et formule des traces
I will first recall the general expectations of Shimura, Langlands, and Kottwtiz on the shape of the zeta function of a Shimura variety, or more generally its etale cohomology. I will then report on some recent progress which partially fulfills these expectations, for Shimura varieties of unitary groups and special orthogonal groups. Finally, I will give a preview of some foreseeable developments in the near future.
