Sheared displays and $p$-divisible groups
We develop a Dieudonné theory for $p$-divisible groups using sheared Witt vectors.
math.NT↗
arXiv subjects
Manuel Hoff
Publications and source records attributed to Manuel Hoff.
Jordan-Chevalley decompositions over imperfect fields
We give a classification of Jordan-Chevalley decompositions of an endomorphism of a finite-dimensional vector space over a not necessarily perfect field, i.e. additive decompositions into commuting semisimple and nilpotent endomorphisms.
math.RT↗
On the Right Derived Functors of Ordinary Parts
We prove a variant of Emerton's conjecture concerning the right derived functors of the ordinary parts functor $\operatorname{Ord}_P^G$. This functor plays an important role in the theory of mod $p$ representations of $p$-adic reductive groups. A key ingredient for our proof is a comparison between certain small and parabolic inductions. Additionally, our method yields an explicit description of Vignéras' right adjoint to parabolic induction. In the appendix (joint with Heyer) we apply our results to obtain a mod $p$ variant of Bernstein's Second Adjointness, i.e. we show that the right and left adjoint of derived parabolic induction are isomorphic (on complexes with admissible cohomology) up to a cohomological shift and twist by a character.
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The EKOR-stratification on the Siegel modular variety with parahoric level structure
We study the arithmetic geometry of the reduction modulo $p$ of the Siegel modular variety with parahoric level structure. We realize the EKOR-stratification on this variety as the fibers of a smooth morphism into an algebraic stack parametrizing homogeneously polarized chains of certain truncated displays.
math.AG↗
Moduli spaces of nilpotent displays
We show that the moduli problem of deformations of nilpotent displays by quasi-isogenies is representable, without using $p$-divisible groups. The main ingredients are Artin's criterion and the theory of truncated displays. This gives in particular a new proof for the representability of Rapoport-Zink spaces.
math.AG↗
On parahoric $(\mathcal{G}, μ)$-displays
We develop tools to study spaces of $p$-divisible groups and Abelian varieties with additional structure. More precisely, we extend the definition of parahoric (Dieudonné) $(\mathcal{G}, μ)$-displays given by Pappas to not necessarily $p$-torsionfree base rings and also introduce the notion of an $(m, n)$-truncated $(\mathcal{G}, μ)$-display. Then we study the deformation theory of Dieudonné $(\mathcal{G}, μ)$-displays. As an application we realize the EKOR stratification of the special fiber of a Kisin-Pappas integral Shimura variety of Hodge type as the fibers of a smooth morphism into the algebraic stack of $(2, 1\text{-}\mathrm{rdt})$-truncated $(\mathcal{G}, μ)$-displays.
math.AG↗