In this article the p-essential dimension of generic symbols over fields of characteristic p is studied. In particular, the p-essential dimension of the length ` generic p-symbol of degree n+1 is bounded below by n + ` when the base field is algebraically closed of characteristic p. The proof uses new techniques for working with residues in Milne–Kato p-cohomology and builds on work of Babic an...

The Lie superalgebras in the extended Freudenthal Magic Square in characteristic 3 are shown to be related to some known simple Lie superalgebras, specific to this characteristic, constructed in terms of orthogonal and symplectic triple systems, which are defined in terms of central simple degree three Jordan algebras.

For a partition λ = {λ1 ≥ λ2 ≥ λ3 ≥ 0} of non-negative integers, we calculate the Euler characteristic of the local system Vλ on the moduli space of genus 3 hyperelliptic curves using a suitable stratification. For some λ of low degree, we make a guess for the motivic Euler characteristic of Vλ using counting curves over finite fields.

We survey algorithms for computing isogenies between elliptic curves defined over a field of characteristic either 0 or a large prime. We introduce a new algorithm that computes an isogeny of degree ` (` different from the characteristic) in time quasi-linear with respect to `. This is based in particular on fast algorithms for power series expansion of the Weierstrass ℘-function and related fu...

The aim of this paper is to examine various interesting results from the theory of general cub~c curves in projective planes of characteristic two. This leads to calculations involving nets of conics in the plane, invariants of the curves, syzygies, and Hessians. It is emphasized that classical methods, (that is those developed for geometries over fields of zero characteristic), do not always s...

In the first section we discuss Morita invariance of differentiable/algebroid cohomology. In the second section we extend the Van Est isomorphism to groupoids. As a first application we clarify the connection between differentiable and algebroid cohomology (proved in degree 1, and conjectured in degree 2 by Weinstein-Xu [50]). As a second application we extend Van Est’s argument for the integra...

In this study, the effect of flame intrinsic instability on the flame structural characteristics of hydrogen/air mixtures premixed at various equivalence ratios were experimentally investigated from the macroscopic and microscopic perspectives, respectively. The correlation degree and the relative deformation degree were defined to quantitatively study the global flame structural characteristic...

We consider degree-biased random walkers whose probability to move from a node to one of its neighbors of degree k is proportional to k(α), where α is a tuning parameter. We study both numerically and analytically three types of characteristic times, namely (i) the time the walker needs to come back to the starting node, (ii) the time it takes to visit a given node for the first time, and (iii)...

Customers have different emotions towards service industries of different natures, leading to inconsistent service quality characteristic items and levels of demands. Different emotions would affect customer perceptions of the customization degree of a hospital (the emotion is relatively sad) and a theme park (the emotion is relatively joyful); while different service quality characteristic-rel...