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Stably rational surfaces over a quasi-finite field
[Surfaces stablement rationnelles sur un corps quasi-fini]
J.-L. Colliot-Thélène CNRS, Université Paris-Sud Université Paris-Saclay,
Département de Mathématiques d'Orsay, France
Аннотация:
Let $k$ be a field and $X$ a smooth, projective, stably $k$-rational surface. If $X$ is split by a cyclic extension, for instance if the field $k$ is finite or more generally quasi-finite, then the surface $X$ is $k$-rational.
Bibliography: 22 titles.
Ключевые слова:
rational surfaces, stable rationality, quasi-finite fields, cyclic splitting, Brauer group.
Поступило в редакцию: 24.01.2018 Исправленный вариант: 13.10.2018
Образец цитирования:
J.-L. Colliot-Thélène, “Stably rational surfaces over a quasi-finite field”, Изв. РАН. Сер. матем., 83:3 (2019), 113–126; Izv. Math., 83:3 (2019), 521–533
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/im8761https://doi.org/10.4213/im8761 https://www.mathnet.ru/rus/im/v83/i3/p113
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