Submission: 2007, Mar 22
Let k be an algebraically closed field of characteristic zero, X a quasi-projective smooth surface over k and A an Azumaya algebra over X of degree n. Using a method suggested by M. Artin, we construct a smooth irreducible quasi-projective surface Y and a flat finite map of degree n of Y onto X such that the pull-back of A to Y is trivial in the Brauer group of Y. We further show that the Galois closure of Y over X is a smooth irreducible quasi-projective surface Z and that the Galois group of k(Z) over k(X) is the symmetric group S(n).
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