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Minimal weights of Hilbert modular forms in characteristic
$p$
Published online by Cambridge University Press: 13 June 2017
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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- Research Article
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- © The Authors 2017
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