Modularity and the Hodge/Tate conjectures for some self-products

Laure Flapan
Thursday, January 23, 2020 - 3:35pm to 4:35pm
Vincent Hall 16

If X is a smooth projective variety over a number field, the Hodge and Tate conjectures describe how information about the subvarieties of X is encoded in the cohomology of X. We explore the role that certain automorphic representations, called algebraic Hecke characters, can play in understanding which cohomology classes of X arise from subvarieties. We use this to deduce the Hodge and Tate conjectures for certain self-products of varieties, including some self-products of K3 surfaces. This is joint work with J. Lang.