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arxiv: 1211.7235 · v5 · pith:USWY64VCnew · submitted 2012-11-30 · 🧮 math.LO

Looking for the lost torus

classification 🧮 math.LO
keywords groupalgebraiccoloureddefinablefieldgreensubgroupadditive
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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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