Minimal weights of Hilbert modular forms in characteristic p

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.

9 pages, to appear in Compositio Mathematica

Cited by in corpus (6)

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• Partial Hasse invariants for Shimura varieties of Hodge-type
• Unramifiedness of weight one Hilbert Hecke algebras