In this short paper, we characterise definable groups in a beautiful pair of models of a stable theory having elimination of imaginaries without the finite cover property: every definable group is (up to isogeny) the extension of the -rational points of a group definable in the theory over by a group definable in .
Furthermore, if is a proper extension of algebraically closed fields, every interpretable group in the pair is, up to isogeny, the extension of the subgroup of -rational points of an algebraic group over by an interpretable group which is the quotient of an algebraic group by the -rational points of an algebraic subgroup.
Dans une belle paire de modèles d’une théorie stable ayant élimination des imaginaires sans la propriété de recouvrement fini, tout groupe définissable se projette, à isogénie près, sur les points -rationnels d’un groupe définissable dans le réduit à paramètres dans . Le noyau de cette projection est un groupe définissable dans le réduit.
Un groupe interprétable dans une paire de corps algébriquement clos où est une extension propre de est, à isogénie près, l’extension des points -rationnels d’un groupe algébrique sur par un groupe interprétable quotient d’un groupe algébrique par les points -rationnels d’un sous-groupe algébrique, le tout défini sur .
@article{CML_2014__6_1_29_0, author = {Thomas Blossier and Amador Martin-Pizarro}, title = {De beaux groupes}, journal = {Confluentes Mathematici}, pages = {29--41}, publisher = {Institut Camille Jordan}, volume = {6}, number = {1}, year = {2014}, doi = {10.5802/cml.11}, zbl = {1323.03039}, language = {fr}, url = {https://cml.centre-mersenne.org/articles/10.5802/cml.11/} }
TY - JOUR TI - De beaux groupes JO - Confluentes Mathematici PY - 2014 DA - 2014/// SP - 29 EP - 41 VL - 6 IS - 1 PB - Institut Camille Jordan UR - https://cml.centre-mersenne.org/articles/10.5802/cml.11/ UR - https://zbmath.org/?q=an%3A1323.03039 UR - https://doi.org/10.5802/cml.11 DO - 10.5802/cml.11 LA - fr ID - CML_2014__6_1_29_0 ER -
Thomas Blossier; Amador Martin-Pizarro. De beaux groupes. Confluentes Mathematici, Volume 6 (2014) no. 1, pp. 29-41. doi : 10.5802/cml.11. https://cml.centre-mersenne.org/articles/10.5802/cml.11/
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