A lower bound on the essential dimension of PGL(4) in characteristic 2

Abstract

In the present paper, we provide a lower bound of the essential dimension over a field of positive characteristic via Kato's cohomology group, defined by cokernel of a general Artin-Schreier operator. Combining this with Tignol's result on the second trace form of simple algebras of degree 4, we show that ed(PGL(4)) >= 4 over a field of characteristic 2.