Philippe Gille: Rationalité du quotient d'une variété de Severi-Brauer par un automorphisme de Kummer.

Submission: 2003, Nov 20

Let S/k be a Severi-Brauer variety defined over a field k. Let f be a Kummer automorphism of S, i.e. an automorphism of order n=dim(S)+1 with finitely many fixed points. If k contains a primitive n-th root of unity, then the field of f-invariant rational functions of S is purely transcendental over k.

2000 Mathematics Subject Classification: 12F20, 14E08.

Keywords and Phrases: Severi-Brauer varieties, rationality, tori, Galois cohomology.

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