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arXiv · 2004.13227

The cone of minimal weights for mod $p$ Hilbert modular forms

Fred Diamond·Payman L Kassaei
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Abstract

We prove that all mod $p$ Hilbert modular forms arise via multiplication by generalized partial Hasse invariants from forms whose weight falls within a certain minimal cone. This answers a question posed by Andreatta and Goren, and generalizes our previous results which treated the case where $p$ is unramified in the totally real field. Whereas our previous work made use of deep Jacquet-Langlands type results on the Goren-Oort stratification (not yet available when $p$ is ramified), here we instead use properties of the stratification at Iwahori level which are more readily generalizable to other Shimura varieties.

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Fred Diamond, Payman L Kassaei. 2020-04-28. The cone of minimal weights for mod $p$ Hilbert modular forms. https://doi.org/10.1093/imrn%2Frnac121

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