The Ax–Schanuel conjecture for variations of Hodge structures
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We extend the Ax–Schanuel theorem recently proven for Shimura varieties by Mok–Pila–Tsimerman to all varieties supporting a pure polarizable integral variation of Hodge structures. In fact, Hodge theory provides a number of conceptual simplifications to the argument. The essential new ingredient is a volume bound for Griffiths transverse subvarieties of period domains.
The first author was partially supported by NSF grant DMS-1702149. We would like to thank the referee for helpful comments and for suggestions which improved the readability of the paper.
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