manuscripta mathematica

, Volume 130, Issue 3, pp 387–409

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

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


Let k be an algebraically closed field. Let P(X11, . . . , Xnn, T) be the characteristic polynomial of the generic matrix (Xij) 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 16H05Secondary 14F22
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© The Author(s) 2009

Authors and Affiliations

  1. 1.IGATEPFLLausanneSwitzerland
  2. 2.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA