Sur les espaces homogènes de Borovoi–Kunyavskii

Nguyễn, Mạnh Linh

doi:10.2140/ant.2024.18.349

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Sur les espaces homogènes de Borovoi–Kunyavskii

Nguyễn Mạnh Linh

Vol. 18 (2024), No. 2, 349–387

DOI: 10.2140/ant.2024.18.349

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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Vol. 18, No. 2, 2024