Algebraic Geometry Seminar: "Algebraic cycles on genus two modular fourfolds"
Abstract: I’ll talk about the Hodge theory of the universal genus two curve with level structure. The main results are that the (1,1) part is spanned by divisors, and the (2,2) part by algebraic cycles, i.e. the Hodge conjecture holds for this variety. If time permits, I’ll discuss the Tate conjecture, which also holds in this case.
Host: Matt Kerr