GTM seminar

Speaker: Kazuhiro Ito (Kavli IPMU)
Title: The Hodge standard conjecture for self-products of K3 surfaces
Date (JST): Thu, May 12, 2022, 15:30 - 17:00
Place: Zoom
Related File: 2797.pdf
Abstract: Grothendieck's standard conjecture, which is a set of conjectures on algebraic cycles, is wide open. In this talk, I will prove the standard conjecture for the square of a K3 surface in positive characteristic. The new part is the Hodge standard conjecture, which predicts certain positivity of the intersection product. Our main ingredient is the Kuga-Satake period map from the moduli space of K3 surfaces to a certain period domain, called the orthogonal Shimura variety. This is joint work with Tetsushi Ito and Teruhisa Koshikawa.