We use de Jong’s conjecture and the existence of ℓ-adic companions to single out integrality properties of the Betti moduli space. The first such instance was in joint work with Michael Groechenig on Simpson’s integrality conjecture for (cohomologically) rigid local systems. This integrality property yields an obstruction for a finitely presented group to be the fundamental group of a sooth quasi-projective complex variety. (joint with Johan de Jong)
This video is part of the Number Theory Web Seminar series.
