# On the Transcendence of Period Images

@inproceedings{Urbanik2021OnTT, title={On the Transcendence of Period Images}, author={David Urbanik}, year={2021} }

Let f : X Ñ S be a family of smooth projective algebraic varieties over a smooth connected base S, with everything defined over Q. Denote by V “ Rf ̊Zpiq the associated integral variation of Hodge structure on the degree 2i cohomology. We consider the following question: when can a fibre Vs above an algebraic point s P SpQq be isomorphic to a transcendental fibre Vs1 with s 1 P SpCqzSpQq? When V induces a quasi-finite period map φ : S Ñ ΓzD, conjectures in Hodge theory predict that such…

## 2 Citations

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Let K Ă C be a number field, and let OK,N “ OKrN s be its ring of N-integers. Recently, Lawrence and Venkatesh proposed a general strategy for proving the Shafarevich conjecture for the fibres of a…

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