Essential dimension of simple algebras in positive characteristic

Abstract

Let p be a prime integer. For any integers 1 <= s <= r, Alg(pr,ps) denotes the class of central simple algebras of degree p(r) and exponent dividing p(s). For any s < r, we find a lower bound for the essential p-dimension of Alg(pr),(ps). Furthermore, we compute an upper bound for Alg(8,2) over a field of characteristic 2. As a result, we show ed(2)(Alg(4,2)) = ed(Alg(4,2)) = 3 and 3 <= ed(Alg(8,2)) <= 10 over a field of characteristic 2. (C) 2011 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.