Minimal weights of Hilbert modular forms in characteristic p
Number Theory
2019-02-20 v2
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.
Keywords
Cite
@article{arxiv.1612.08725,
title = {Minimal weights of Hilbert modular forms in characteristic p},
author = {Fred Diamond and Payman Kassaei},
journal= {arXiv preprint arXiv:1612.08725},
year = {2019}
}
Comments
9 pages, to appear in Compositio Mathematica