Jake Huryn
The Ohio State University
Title
On the torsion in the Chow motive of an Enriques surface
Abstract
The category of Chow motives is a sort of universal Z-linearization of the category of smooth projective varieties. It turns out that this category contains torsion objects, i.e. objects M for which (End(M),+) is a torsion group; these appear to have been studied very little and are poorly understood. The simplest examples occur as direct summands in the motives of Enriques surfaces. In this talk, I will describe progress toward the following questions.
1. To what extent is an Enriques surface determined by its torsion motive?
2. When are these torsion motives irreducible?
These questions can be translated into cases of the integral Hodge and Tate conjectures. Our methods rely on, in particular, some pieces of the theory of elliptic curves.
This is joint work with Will Newman.