, Volume 130, Issue 3, pp 387-409,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 10 Sep 2009

Singularities of generic characteristic polynomials and smooth finite splittings of Azumaya algebras over surfaces


Let k be an algebraically closed field. Let P(X 11, . . . , X nn , T) be the characteristic polynomial of the generic matrix (X ij ) over k. We determine its singular locus as well as the singular locus of its Galois splitting. If X is a smooth quasi-projective surface over k and A an Azumaya algebra on X of degree n, using a method suggested by M. Artin, we construct finite smooth splittings for A of degree n over X whose Galois closures are smooth.