Corpus ID: 119322343

Overconvergent Hilbert modular forms via perfectoid modular varieties

@article{Birkbeck2019OverconvergentHM,
  title={Overconvergent Hilbert modular forms via perfectoid modular varieties},
  author={C. Birkbeck and Ben Heuer and Chris Williams},
  journal={arXiv: Number Theory},
  year={2019}
}

C. Birkbeck, Ben Heuer, Chris Williams

Published 2019

Mathematics

arXiv: Number Theory

We give a new construction of $p$-adic overconvergent Hilbert modular forms by using Scholze's perfectoid modular varieties at infinite level and the Hodge--Tate period map. The definition is analytic, closely resembling that of complex Hilbert modular forms as holomorphic functions satisfying a transformation property under congruence subgroups. As a special case, we first treat elliptic modular forms, extending recent work of Chojecki, Hansen and Johansson. We then construct sheaves of both… CONTINUE READING

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