Surfaces stablement rationnelles sur un corps quasi-fini
Algebraic Geometry
2018-06-19 v2
Abstract
If a smooth, geometrically rational surface over a finite field is not rational over that field, then over some finite extension of that field the Brauer group of the surface is nonzero. In particular such a surface is not stably rational. This is a special case of a general statement about geometrically rational surfaces which split over a cyclic extension of their field of definition.
Keywords
Cite
@article{arxiv.1711.09595,
title = {Surfaces stablement rationnelles sur un corps quasi-fini},
author = {Jean-Louis Colliot-Thélène},
journal= {arXiv preprint arXiv:1711.09595},
year = {2018}
}
Comments
In French; revised version, 14th June 2018