Voir la notice de l'article provenant de la source Numdam
In this note, we check that a complex projective algebraic variety has (at most) countably many real forms. We more generally prove it when the field of reals is replaced with a field that has only countably many finite extensions up to isomorphism. The verification consists in gathering known results about automorphism groups and Galois cohomology. This contrasts with the recent discovery by A. Bot of an affine real variety with uncountably many real forms.
CC-BY 4.0
@article{CRMATH_2023__361_G5_863_0,
author = {Labinet, Timoth\'ee L.},
title = {Projective varieties have countably many real forms},
journal = {Comptes Rendus. Math\'ematique},
pages = {863--867},
publisher = {Acad\'emie des sciences, Paris},
volume = {361},
number = {G5},
year = {2023},
doi = {10.5802/crmath.441},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/crmath.441/}
}
TY - JOUR AU - Labinet, Timothée L. TI - Projective varieties have countably many real forms JO - Comptes Rendus. Mathématique PY - 2023 SP - 863 EP - 867 VL - 361 IS - G5 PB - Académie des sciences, Paris UR - http://geodesic.mathdoc.fr/articles/10.5802/crmath.441/ DO - 10.5802/crmath.441 LA - en ID - CRMATH_2023__361_G5_863_0 ER -
%0 Journal Article %A Labinet, Timothée L. %T Projective varieties have countably many real forms %J Comptes Rendus. Mathématique %D 2023 %P 863-867 %V 361 %N G5 %I Académie des sciences, Paris %U http://geodesic.mathdoc.fr/articles/10.5802/crmath.441/ %R 10.5802/crmath.441 %G en %F CRMATH_2023__361_G5_863_0
Labinet, Timothée L. Projective varieties have countably many real forms. Comptes Rendus. Mathématique, Tome 361 (2023) no. G5, pp. 863-867. doi: 10.5802/crmath.441
Cité par Sources :