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Sur les espaces homogènes de Borovoi–Kunyavskii

Nguyễn Mạnh Linh

Vol. 18 (2024), No. 2, 349–387
Abstract

Nous établissons le principe de Hasse et l’approximation faible pour certains espaces homogènes de SL m à stabilisateur géométrique nilpotent de classe 2, construits par Borovoi et Kunyavskii. Ces espaces homogènes vérifient donc une conjecture de Colliot-Thélène concernant l’obstruction de Brauer–Manin pour les variétés géométriquement rationnellement connexes.

We establish the Hasse principle and the weak approximation property for certain homogeneous spaces of SL m whose geometric stabilizer is of nilpotency class 2, which were constructed by Borovoi and Kunyavskii. These homogeneous spaces verify thus a conjecture of Colliot-Thélène on the Brauer–Manin obstruction for geometrically rationally connected varieties.

Keywords
Galois cohomology, lien, nonabelian cohomology, homogeneous spaces, rational points, Hasse principle, weak approximation, Brauer–Manin obstruction
Mathematical Subject Classification
Primary: 11R34, 14G05, 14G12
Milestones
Received: 15 July 2022
Revised: 22 December 2022
Accepted: 13 February 2023
Published: 6 February 2024
Authors
Nguyễn Mạnh Linh
Laboratoire de mathématiques d’Orsay
Université Paris-Saclay
Orsay
France

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