We compute the image of the p-adic period map for polarized K3 surfaces with supersingular reduction. This gives rise to a Rapoport-Zink type uniformization of their moduli space by an explicit open rigid analytic subvariety of a local Shimura variety of orthogonal type. In contrast to the case of Rapoport-Zink uniformization of Shimura varieties and in analogy to the complex case, the uniformizing domain does not carry an action of a p-adic Lie group, but only of a discrete subgroup. We briefly sketch how the same arguments can be applied to obtain a uniformization for the moduli space of smooth cubic fourfolds with supersingular reduction.

We introduce the notion of dR-absolutely special subvarieties in motivic variations of Hodge structure as special subvarieties cut out by (de Rham)-absolute Hodge cycles and conjecture that all special subvarieties are dR-absolutely special. This is implied by Deligne's conjecture that all Hodge cycles are absolute Hodge cycles, but is a much weaker conjecture. We prove our conjecture for subvarieties satisfying a simple monodromy condition introduced in [KOU20]. We study applications to typical respectively atypical intersections and Q-bialgebraic subvarieties. Finally, we show that Deligne's conjecture as well as ours can be reduced to the case of special points in motivic variations.Conjecture 0.5. Every special subvariety is dR-absolutely special.

We introduce ℓ-Galois special subvarieties as an ℓ-adic analogue of the Hodgetheoretic notion of a special subvariety. The Mumford-Tate conjecture predicts that both notions are equivalent. We prove this equivalence for subvarieties satisfying a simple monodromy condition. As an application we see that if the derived group of the generic Mumford-Tate group of a family is simple, then the positive part of the Hodge locus coincides with the positive part of the ℓ-Galois exceptional locus. Finally, we show that the Mumford-Tate conjecture for abelian varieties is equivalent to a conjecture about the existence of positive dimensional algebraic subvarieties in Shimura varieties with certain Galois theoretic properties.

This article presents the impact of displaying accurate or inaccurate position estimates on air mission commanders’ (AMC) situation awareness (SA) during datalink interruptions between AMC and unmanned aerial vehicles (UAVs). The lack of current information about UAV state and position during datalink interruptions is suspected to negatively influence the controlling AMC's SA. We assume that the AMC's SA can be supported by displaying a state estimate, based on last transmitted data, instead of displaying last known position. An experimental evaluation in a full‐mission research cockpit simulator showed improvements in subjective SA with estimate shown. Objective SA only improved, if the estimate was accurate. Although we expected a negative impact of inaccurate estimates on objective SA (since the user might falsely trust it), none could be observed. Improvements in SA with accurate estimates, but no observable degradations with inaccurate estimates suggest benefits of showing an estimate in any case.