Seminar in Algebraic Geometry and Number Theory

Abstract: Tautological rings of Shimura varieties are subrings of the Chow ring which contain many interesting classes and are open to computation. I'll present a conjecture describing these tautological rings in characteristic p and provide some basic evidence for it. Part of this evidence is a theorem describing the tautological ring of a Hilbert modular variety at an unramified prime, whose proof I'll explain. The techniques are exclusive to characteristic p and make use of the theory of G-Zips.