Related papers: Property tau in positive characteristic

In this paper we give a construction for a special type of congruences on commutative semigroups. We apply our result for the multiplicative semigroup of all positive integers.

Let K be a global field of characteristic not 2. Let Z be a symmetric variety defined over K and S a finite set of places of K. We obtain counting and equidistribution results for the S-integral points of Z. Our results are effective when K…

In this paper, among other things, we state and prove the mean ergodic theorem for amenable semigroup algebras.

We prove a ratio ergodic theorem for amenable equivalence relations satisfying a strong form of the Besicovich covering property. We then use this result to study general non-singular actions of non-abelian free groups and establish a ratio…

We examine the extent to which sublinear-sample property testing and estimation apply to settings where samples are independently but not identically distributed. Specifically, we consider the following distributional property testing…

We prove an equidistribution theorem a la Bader-Muchnik for operator-valued measures associated with boundary representations in the context of discrete groups of isometries of CAT(-1) spaces thanks to an equidistribution theorem of T.…

In this short article, we obtained some equivalent formulations of property $T$ for a general locally compact quantum group $\mathbb{G}$, in terms of the full quantum group $C^*$-algebras $C_0^\mathrm{u}(\widehat{\mathbb{G}})$ and the…

We give a group theoretic proof of the splitting of sharply 2-transitive groups of characteristic 3.

In this note we prove a variational open adelic image theorem for the Galois action on the cohomology of smooth proper $S$-schemes where $S$ is a smooth variety over a finitely generated field of positive characteristic. A central tool is a…

We propose a fairness measure relaxing the equality conditions in the popular equal odds fairness regime for classification. We design an iterative, model-agnostic, grid-based heuristic that calibrates the outcomes per sensitive attribute…

We give a new proof of the Mordell-Lang conjecture in positive characteristic for finitely generated subgroups. We also make some progress towards the full Mordell-Lang conjecture in positive characteristic.

The object of this short note is to prove a theorem and present a conjecture for the number of even entries in the character table of the symmetric group.

Numerical semigroup rings are investigated from the relative viewpoint. It is known that algebraic properties such as singularities of a numerical semigroup ring are properties of a flat numerical semigroup algebra. In this paper, we show…

We establish an equidistribution theorem for the zeros of random holomorphic sections of high powers of a positive holomorphic line bundle. The equidistribution is associated with a family of singular moderate measures. We also give a…

We present a non-standard proof of the fact that the existence of a local (i.e. restricted to a point) characteristic-zero, semi-parametric lifting for a variety defined by the zero locus of polynomial equations over the integers is…

A number has the "collective" property if the number is the greatest lower bound of a bounded, strictly decreasing sequence on the real line. We prove that numbers with the collective property constitute an empty set.

A Tauberian theorem deduces an asymptotic for the partial sums of a sequence of non-negative real numbers from analytic properties of an associated Dirichlet series. Tauberian theorems appear in a tremendous variety of applications, ranging…

We study when the fiber product of groups with Property (T) has Property (T).

Using the projection complex machinery, Bestvina-Bromberg-Fujiwara, Hagen-Petyt and Han-Nguyen-Yang prove that several classes of nonpositively-curved groups admit equivariant quasi-isometric embeddings into finite products of quasi-trees,…

We give an optimal necessary and sufficient condition for the quotient polynomial and remainder in the division algorithm to have positive coefficients.