Algebraic Geometry Seminar | Philip Engel (UIC)

Title: Local systems underlying variation of Hodge structure

Abstract: Generalizing finiteness theorems of Parshin, Arakelov, and Faltings, 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. Deligne conjectured that an appropriate form of this finiteness also holds in families of quasiprojective varieties. In the 1990's, Simpson refined this conjecture in the following form: the nonabelian Hodge locus is algebraic. I will discuss joint work with Salim Tayou that these conjectures are true when the algebraic monodromy group is cocompact.

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