Algebraic Cycles, L-Values, and Euler Systems "Shimura Varieties and L-Functions" Topical Workshop: Zeta Functions of Shimura Varieties: Past, Present, and the Near Future

March 16, 2023
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.