Back to Algebraic Geometry Seminar: Spring 2018
Algebraic Geometry Seminar
Date: Tuesday, Apr 3, 2018
Time: 3:30PM - 4:30PM
Location: LCB 222
Sarah Frei
University of Oregon
Title |
Moduli spaces of sheaves on a K3 surface and Galois representations |
Abstract |
For a fixed K3 surface, we can study various moduli spaces of sheaves having a given topological type. Under appropriate conditions on the topological data, the moduli spaces are smooth projective varieties. I will discuss a new result about the geometry and arithmetic of these moduli spaces when the K3 surface is defined over an arbitrary field. For any two such moduli spaces of the same dimension, their étale cohomology groups with $\mathbb{Q}_\ell$-coefficients are isomorphic as Galois representations. In particular, when the K3 surface is defined over a finite field, this implies that the moduli spaces have equal zeta functions. |
Algebraic Geometry