We introduce a presentation for central simple algebras over a field k using Amitsur
cohomology. We provide efficient algorithms for computing a cocycle corresponding to any …

We consider the algorithmic problem of computing a primitive idempotent of a central simple
algebra over the field of rational functions over a finite field. The algebra is given by a set of …

arXiv:2111.08569v1 [math.NT] 16 Nov 2021 Page 1 arXiv:2111.08569v1 [math.NT] 16 Nov
2021 ISOTROPIC VECTORS OVER GLOBAL FIELDS PRZEMYSŁAW KOPROWSKI Abstract …

We present an efficient computational representation of central simple algebras using
Brauer factor sets. Using this representation and polynomial quantum algorithms for number …

We propose polynomial-time algorithms for finding nontrivial zeros of quadratic forms with
four variables over rational function fields of characteristic 2. We apply these results to find …

Let L be a separable quadratic extension of either Q \documentclass[12pt]{minimal} \usepackage{amsmath}
\usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} …

We propose polynomial-time algorithms for finding nontrivial zeros of quadratic forms with
four variables over rational function fields of characteristic 2. We apply these results to find …

In this thesis we consider the following algorithmic problem. Let K be a field and let A be an
algebra over K which is given by structure constants and is isomorphic to Mn (K), the algebra …

Let C be a smooth, projective and geometrically connected curve defined over a finite field
Fq. Given a semisimple C− S-group scheme G where S is a finite set of closed points of C …