We say that a smooth algebraic group over a field is very special if for any field extension , every -homogeneous -variety has a -rational point. It is known that every split solvable linear algebraic group is very special. In this note, we show that the converse holds, and discuss its relationship with the birational classification of algebraic group actions.
Nous disons qu’un groupe algébrique lisse sur un corps est très spécial si pour toute extension de corps , toute -variété homogène sous a un point -rationnel. On sait que tout groupe linéaire résoluble scindé est très spécial. Dans cette note, nous obtenons la réciproque et nous discutons ses relations avec la classification birationnelle des actions de groupes algébriques.
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@article{CRMATH_2020__358_6_713_0, author = {Brion, Michel and Peyre, Emmanuel}, title = {Very special algebraic groups}, journal = {Comptes Rendus. Math\'ematique}, pages = {713--719}, publisher = {Acad\'emie des sciences, Paris}, volume = {358}, number = {6}, year = {2020}, doi = {10.5802/crmath.86}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/crmath.86/} }
TY - JOUR AU - Brion, Michel AU - Peyre, Emmanuel TI - Very special algebraic groups JO - Comptes Rendus. Mathématique PY - 2020 SP - 713 EP - 719 VL - 358 IS - 6 PB - Académie des sciences, Paris UR - http://archive.numdam.org/articles/10.5802/crmath.86/ DO - 10.5802/crmath.86 LA - en ID - CRMATH_2020__358_6_713_0 ER -
Brion, Michel; Peyre, Emmanuel. Very special algebraic groups. Comptes Rendus. Mathématique, Volume 358 (2020) no. 6, pp. 713-719. doi : 10.5802/crmath.86. http://archive.numdam.org/articles/10.5802/crmath.86/
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