| Résume | Let f:X\to S be a quasi-projective family of varieties defined over Qbar. We prove that the points of S(Qbar) that are Hodge generic for the variation of Hodge structures associated to f are analytically dense in S. More generally, motivated by the Grothendieck period conjecture and under a large-monodromy assumption, we establish the density of algebraic points at which the periods of the fibre satisfy no unexpected relations of degree at most delta. The main technical input is a new result on relations among solutions of G-operators, based on height estimates of Bombieri and André. This is a joint work with Gal Binyamini and David Urbanik.
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