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The Ax–Schanuel conjecture for variations of Hodge structures

  • Benjamin BakkerEmail author
  • Jacob Tsimerman
Article
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Abstract

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.

Notes

Acknowledgements

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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GeorgiaAthensUSA
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

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