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arXiv · 1306.5849

De Beaux Groupes

Thomas Blossier·Amador Martin-Pizarro
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Abstract

In this short paper, we will provide a characterisation of interpretable groups in a beautiful pair (K, E) of algebraically closed fields : every interpretable group is, up to isogeny, the extension of the subgroup of E-rational points of an algebraic group by an interpretable group which is the quotient of an algebraic group by the E-rational points of an algebraic subgroup.---Dans une belle paire (K;E) de corps algébriquement clos, un groupe définissable se projette, à isogénie près, sur les points E-rationnels d'un groupe algébrique ayant pour noyau un groupe algébrique. Un groupe interprétable est, à isogénie près, l'extension des points E-rationnels d'un groupe algébrique par un groupe interprétable, qui est lui le quotient d'un groupe algébrique par les points E-rationnels d'un sous-groupe algébrique.

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Thomas Blossier, Amador Martin-Pizarro. 2014-05-22. De Beaux Groupes. https://arxiv.org/abs/1306.5849

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