Diophantine Properties of the Betti Moduli Space

We prove in particular that when the Betti moduli space of a smooth quasi-projective variety over the complex numbers with some quasi-unipotent monodromies at infinity and finite determinant is irreducible over the integers and over the complex numbers, then it possesses an integral point. A more general version of the theorem yields a new obstruction for the finitely presented group to be the topological fundamental group of a smooth complex quasi-projective variety.

(Joint with J. de Jong, based in part on joint work with M. Groechenig).

Pretalk: Ben Church will discuss some of the concepts used in the proof and the formulation of the statement. 2:00-2:45pm in SC 530

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For more info, see https://researchseminars.org/seminar/HarvardNT