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arXiv · 1612.08725

Minimal weights of Hilbert modular forms in characteristic p

Fred Diamond·Payman Kassaei
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Abstract

We consider mod p Hilbert modular forms associated to a totally real field of degree d in which p is unramified. We prove that every such form arises by multiplication by partial Hasse invariants from one whose weight (a d-tuple of integers) lies in a certain cone contained in the set of non-negative weights, answering a question of Andreatta and Goren. The proof is based on properties of the Goren-Oort stratification on mod p Hilbert modular varieties established by Goren and Oort, and Tian and Xiao.

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Fred Diamond, Payman Kassaei. 2016-12-27. Minimal weights of Hilbert modular forms in characteristic p. https://doi.org/10.1112/s0010437x17007230

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