Event Type
Seminar
Monday, November 8, 2021 12:30 PM
Brian Lawrence (UCLA)

Interesting moduli spaces don't have many integral points.  More precisely, if X is a variety over a number field, admitting a variation of Hodge structure whose associate period map is injective, then the number of S-integral points on X of height at most H grows more slowly than H^{\epsilon}, for any positive \epsilon.  This is a sort of weak generalization of the Shafarevich conjecture; it is a consequence of a point-counting theorem of Broberg, and the largeness of the fundamental group of X.  Joint with Ellenberg and Venkatesh.
https://arxiv.org/abs/2109.01043