Looking for the lost torus

Thomas Blossier; Amador Martin-Pizarro; Frank Olaf Wagner

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arXiv · 1211.7235

Looking for the lost torus

Thomas Blossier·Amador Martin-Pizarro·Frank Olaf Wagner

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Abstract

We classify the groups definable in the coloured fields obtained by Hrushovski amalgamation. A group definable in the bad green field is isogenous to the quotient of a subgroup of an algebraic group by a Cartesian power of the group of green elements. A definable subgroup of an algebraic group in the green or red field is an extension of the coloured points of a multiplicative or additive algebraic group by an algebraic group. In particular, a simple group in a coloured field is algebraic.

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Thomas Blossier, Amador Martin-Pizarro, Frank Olaf Wagner. 2012-11-30. Looking for the lost torus. https://arxiv.org/abs/1211.7235

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