On the Hasse invariant of Hilbert modular varieties mod $p$

Autor:	Reppen, Stefan
Rok vydání:	2023
Předmět:	Mathematics - Algebraic Geometry Mathematics - Number Theory
Druh dokumentu:	Working Paper
Popis:	Let $F$ be a totally real field and let $S$ denote the geometric special fiber of a Hilbert modular variety associated to $F$, at a prime unramified in $F$. We show that the order of vanishing of the Hasse invariant on $S$ is equal to the largest integer $m$ such that the smallest piece of the conjugate filtration lies in the $m^{\text{th}}$ piece of the Hodge filtration. This result is a direct analogue of Ogus' on families of Calabi-Yau varieties in positive characteristic. We also show that the order of vanishing at a point is the same as the codimension of the Ekedahl-Oort stratum containing it. Comment: To appear in J. Algebra
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2306.15224 Zobrazit plný text záznamu View this record from Arxiv