Workshop: Sparsity of Integral Points on Moduli Spaces of Varieties

Date: 2021-10-22

Time: 09:45 - 10:45

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Brian Lawrence


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.