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Izvestiya: Mathematics, 2019, Volume 83, Issue 3, Pages 521–533
DOI: https://doi.org/10.1070/IM8761 (Mi im8761) 		 
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
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DOI: https://doi.org/10.1070/IM8761
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.
Received: 24.01.2018
Revised: 13.10.2018
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2019, Volume 83, Issue 3, Pages 113–126
DOI: https://doi.org/10.4213/im8761
Bibliographic databases:
Document Type: Article
UDC: 512.77
MSC: 14M20, 14E08, 14J26, 14F22
Language: English
Original paper language: French
Citation: J.-L. Colliot-Thélène, “Stably rational surfaces over a quasi-finite field”, Izv. RAN. Ser. Mat., 83:3 (2019), 113–126; Izv. Math., 83:3 (2019), 521–533
Citation in format AMSBIB
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:27
    English version PDF:15
    References:36
    First page:28
     
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