The Hodge locus

Abstract: I will report on a joint work with Klingler and Ullmo. Given a polarizable variation of Hodge structures on a smooth complex quasi-projective variety $S$ (e.g. the one associated to a family of pure motives over $S$), Cattani, Deligne and Kaplan proved that its Hodge locus (the locus of closed points of $S$ where exceptional Hodge tensors appear) is a countable union of closed algebraic subvarieties of $S$. In this talk I will discuss when this Hodge locus is actually algebraic.

If time permits I will explain how such an algebraicity result complements the Lawrence-Venkatesh method.

algebraic geometrynumber theory

Audience: researchers in the topic

Séminaire de géométrie arithmétique et motivique (Paris Nord)