Stably rational surfaces over a quasi-finite field

J.-L. Colliot-Thélène

CNRS, Université Paris-Sud Université Paris-Saclay, Département de Mathématiques d'Orsay, France

Abstract: Let $k$ be a field and $X$ a smooth, projective, stably $k$-rational surface. If $X$ is split by a cyclic extension (for example, if the field $k$ is finite or, more generally, quasi-finite), then the surface $X$ is $k$-rational.

Keywords: rational surfaces, stable rationality, quasi-finite fields, cyclic splitting, Brauer group.

UDC: 512.77

MSC: 14M20, 14E08, 14J26, 14F22

Received: 24.01.2018
Revised: 13.10.2018

Language: French

DOI: 10.4213/im8761

 English version: Izvestiya: Mathematics, 2019, 83:3, 521–533

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