Caltech/USC Joint Algebra and Geometry Seminar

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 values show up. Joint work with Tony Feng and Wei Zhang.