arXiv subjects
Publications and source records attributed to Oliver Bueltel.
Let $k_0$ be a finite field of characteristic $p$, let $G$ be a smooth affine group scheme over $\mathbb{Z}_p$, and let $μ$ be a cocharacter of $G_{W(k_0)}$ such that the set of $μ$-weights of $\text{Lie}\, G$ is a subset of $\{-1,0,1,2,\dots\}$. We prove that the groupoid of adjoint nilpotent $(G,μ)$-displays is equivalent to the groupoid of $(G,μ)$-windows, which are the generalizations of windows.
This work settles the Eichler-Shimura congruence relation of Blasius and Rogawski for certain 5-dimensional Hodge-type Shimura varieties, that were not tractable by previously known methods. In a more general context we introduce a hypothesis called (NVC) on the behavior of Hecke correspondences, and show that it implies the congruence relation. A major ingredient in the proof of this result is a theorem of R.Noot on CM-lifts of ordinary points in characteristic p, along with an analysis of the mod p-reductions of various Hecke translates of that CM-lift. Finally we prove this (NVC)-hypothesis for our particular Shimura 5-folds, and in doing so we obtain an unconditional result for the congruence relation of these non-PEL examples.
We study properties of a map from a certain unitary group in $n$ variables to a related unitary group in $\binom{n}{k}$ variables. We explain how it gives rise to a map between canonical models of Shimura varieties and we prove that it extends to the ordinary locus of the integral model. Finally we extend results of Satake on the endomorphism ring of a generic image point to positive characteristics.
Let $ρ$ be a finite-dimensional faithful representation of a semisimple algebraic group $G$. By means of a deformation argument, we show that there exists a family of Abelian varieties over a smooth and projective curve over the algebraic closure of a prime field of positive characteristic, such that its $\ell$-adic monodromy group covers $G$ and its $\ell$-adic monodromy representation contains $ρ$.
The paper studies the supersingular locus of the characteristic p moduli space of principally polarized abelian 8-folds that are equipped with an action of a maximal order in a quaternion algebra, that is non-split at the infinite place, but split at p. The main result is that its irreducible components are Fermat surfaces of degree p+1.