Algebraic Geometry Seminar: The tautological ring for the moduli of Shtukas

The tautological ring for the moduli of Shtukas

Abstract: Many well-known moduli spaces have tautological classes, and it is an important question to study the structure of the subring they generate in cohomology. In this talk, we examine the tautological ring for the moduli of Shtukas, the function field analog of Shimura varieties. We define a "phantom" tautological ring that corrects the non-compactness of the moduli space. We obtain an analog of Hirzebruch proportionality (originally for Hermitian locally symmetric spaces) in our setting, where higher derivatives of zeta functions show up. Joint work with Tony Feng and Wei Zhang.