Essential dimension of central simple algebras

Abstract

Let p be a prime integer, 1≤s≤r be integers and F be a field of characteristic different from p. We find upper and lower bounds for the essential p-dimension ed_p($ Al{{g}_{{{{p}^r},{{p}^s}}}} $) of the class $ Al{{g}_{{{{p}^r},{{p}^s}}}} $ of central simple algebras of degree p^r and exponent dividing p^s. In particular, we show that ed(Alg_8,2)=ed₂(Alg_8,2)=8 and ed_p($ Al{{g}_{{{{p}^2},p}}} $)=p²+p for p odd.