Appears in collection : Arithmetic and Diophantine Geometry, via Ergodic Theory and o-minimality

We explain how a theory of infinitesimal period maps can be used to "transfer" Hodge-theoretic unlikely intersection results from characteristic zero to positive characteristic for sufficiently large primes p. We survey several results of this type and give an idea of the methods used to prove them. Partially joint work with Ziquan Yang.