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, Volume 130, Issue 3, pp 387–409 | Cite as

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

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Abstract

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 16H05 Secondary 14F22 

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Copyright information

© The Author(s) 2009

Authors and Affiliations

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

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