Refined partial Hasse invariants and the canonical filtration
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Supporting information
Author(s)
Bijakowski, S
Type
Working Paper
Abstract
Let $G$ be a $p$-divisible group over a scheme of characteristic $p$, and
assume that it is endowed with an action of the ring of integers of a finite
unramified extension $F$ of $\mathbb{Q}_p$. Let us fix the type $\mu$ of this action on the sheaf of differentials $\omega_G$. V. Hernandez, following a construction of Goldring and Nicole, defined partial Hasse invariants for $G$. These are sections of invertible sheaves. The product of these invariants is the $\mu$-ordinary Hasse invariant, and it is non-zero if and only if the $p$-divisible group is $\mu$-ordinary (i.e. the Newton polygon is minimal given the type of the action). We show that, if one assumes the existence of a certain filtration refining the Hodge filtration, each of these partial Hasse invariants can be expressed as a product of other sections, the refined partial Hasse invariants. Over a Shimura variety, the condition is satisfied if one considers an explicit closed subscheme of a certain flag variety. As an application, we relate these refined partial Hasse invariants to the partial degrees of the canonical filtration (if it exists).
assume that it is endowed with an action of the ring of integers of a finite
unramified extension $F$ of $\mathbb{Q}_p$. Let us fix the type $\mu$ of this action on the sheaf of differentials $\omega_G$. V. Hernandez, following a construction of Goldring and Nicole, defined partial Hasse invariants for $G$. These are sections of invertible sheaves. The product of these invariants is the $\mu$-ordinary Hasse invariant, and it is non-zero if and only if the $p$-divisible group is $\mu$-ordinary (i.e. the Newton polygon is minimal given the type of the action). We show that, if one assumes the existence of a certain filtration refining the Hodge filtration, each of these partial Hasse invariants can be expressed as a product of other sections, the refined partial Hasse invariants. Over a Shimura variety, the condition is satisfied if one considers an explicit closed subscheme of a certain flag variety. As an application, we relate these refined partial Hasse invariants to the partial degrees of the canonical filtration (if it exists).
Date Issued
2016-12-15
Citation
2016
Copyright Statement
© 2016 The Author.
Identifier
http://arxiv.org/abs/1612.05078v1
Subjects
math.NT
math.NT
math.AG
Notes
20 pages