Philip Engel : Local systems underlying variation of Hodge structure

Posted by Philip Engel , part of the Algebraic Geometry Seminar.

At

Sept. 9, 2024, 3 p.m.

In

636 SEO

Abstract

Deligne proved in 1987 that only finitely many Z-local systems of a fixed rank underlie a polarized variation of Hodge structure, over a fixed quasiprojective variety. He conjectured that this finiteness also holds in families of quasiprojective varieties. In the 1990’s, Simpson’s refined this conjecture in the following form: the nonabelian Hodge locus is algebraic. I will discuss joint work with Salim Tayou proving these conjectures when the algebraic monodromy group is cocompact.