manuscripta mathematica

, Volume 130, Issue 3, pp 387–409

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

Authors

    • IGATEPFL
  • Raman Parimala
    • Department of Mathematics and Computer ScienceEmory University
Open AccessArticle

DOI: 10.1007/s00229-009-0295-y

Cite this article as:
Ojanguren, M. & Parimala, R. manuscripta math. (2009) 130: 387. doi:10.1007/s00229-009-0295-y

Abstract

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.

Mathematics Subject Classification (2000)

Primary 16H05 Secondary 14F22

Copyright information

© The Author(s) 2009