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arXiv · 1711.09595

Surfaces stablement rationnelles sur un corps quasi-fini

Jean-Louis Colliot-Thélène
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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.

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Jean-Louis Colliot-Thélène. 2017-11-27. Surfaces stablement rationnelles sur un corps quasi-fini. https://arxiv.org/abs/1711.09595

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