Essential dimension of central simple algebras

Abstract

Let p be a prime integer, 1a parts per thousand currency signsa parts per thousand currency signr 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) () of the class of central simple algebras of degree p (r) and exponent dividing p (s) . In particular, we show that ed(Alg (8,2))=ed(2)(Alg (8,2))=8 and ed (p) ()=p (2)+p for p odd.