Looking for the lost torus

A la recherche du tore perdu

Thomas Blossier (1) , Amador Martin-Pizarro (1) , Frank Olaf Wagner (2)

1 AGL - Algèbre, géométrie, logique
2 ICJ - Institut Camille Jordan

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 a Cartesian power of the subgroup of coloured elements by an algebraic group. In particular, a simple group in a coloured field is algebraic.

Mots clés: Model Theory; amalgamation method; flatness; interpretation; group; algebraic group; bad field; bad group

Domaines: Logique [math.LO]

Thomas Blossier, Amador Martin-Pizarro, Frank Olaf Wagner. A la recherche du tore perdu. 2013. ⟨hal-00758982v3⟩