In this paper, for a smooth variety X equipped with an action of a connected algebraic group G (not necessary linear), we introduce the notion of invariant Brauer sub-group and the notion of invariant étale Brauer–Manin obstruction. Then we prove that this obstruction is equivalent to the étale Brauer–Manin obstruction. This extends the main notion and the key result of author’s previous article and this also extends a result of B. Creutz.
Dans cet article, pour une variété lisse X munie d’une action d’un groupe algébrique connexe G (non nécessairement linéaire), on introduit la notion de sous-groupe de Brauer invariant et la notion d’obstruction de Brauer–Manin étale invariante. Ensuite, on montre que cette obstruction équivaut à l’obstruction de Brauer–Manin étale. Ceci généralise la notion principale et le résultat clé de l’aticle précédent de l’auteur et ceci généralise aussi un résultat de B. Creutz.
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Mot clés : Groupe algébrique, groupe de Brauer, principe de Hasse.
Keywords: Algebraic group, Brauer group, Hasse principle.
Cao, Yang 1
@article{AIF_2024__74_2_627_0, author = {Cao, Yang}, title = {Sous-groupe de {Brauer} invariant pour un groupe alg\'ebrique connexe quelconque}, journal = {Annales de l'Institut Fourier}, pages = {627--661}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {74}, number = {2}, year = {2024}, doi = {10.5802/aif.3590}, language = {fr}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3590/} }
TY - JOUR AU - Cao, Yang TI - Sous-groupe de Brauer invariant pour un groupe algébrique connexe quelconque JO - Annales de l'Institut Fourier PY - 2024 SP - 627 EP - 661 VL - 74 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3590/ DO - 10.5802/aif.3590 LA - fr ID - AIF_2024__74_2_627_0 ER -
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Cao, Yang. Sous-groupe de Brauer invariant pour un groupe algébrique connexe quelconque. Annales de l'Institut Fourier, Volume 74 (2024) no. 2, pp. 627-661. doi : 10.5802/aif.3590. https://aif.centre-mersenne.org/articles/10.5802/aif.3590/
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