Singularities of generic characteristic polynomials and smooth finite splittings of Azumaya algebras over surfaces. (Q1034711)

Let \(A_n\) be the ring of generic \(n\times n\) matrices over an algebraically closed field \(K\), modulo the characteristic polynomial. It is shown that the codimension of the singular locus of \(A_n\) is 3. Similarly, the singular locus of the Galois splitting is considered. Artin's method is used to construct smooth splittings \(Y\to X\) of Azumaya algebras over a smooth quasi-projective surface \(X\) over \(K\), having a smooth irreducible Galois closure.