English

Looking for the lost torus

Logic 2015-01-20 v5

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.

Keywords

Cite

@article{arxiv.1211.7235,
  title  = {Looking for the lost torus},
  author = {Thomas Blossier and Amador Martin-Pizarro and Frank Olaf Wagner},
  journal= {arXiv preprint arXiv:1211.7235},
  year   = {2015}
}

Comments

in French

R2 v1 2026-06-21T22:46:46.821Z