Die böse Farbe

Andreas Baudisch (1) , Martin Hils (2) , Amador Martin-Pizarro (3) , Frank Olaf Wagner (4)

1 Institut für Mathematik [Berlin]
2 ELM - Equipe de Logique Mathématique
3 AGL - Algèbre, géométrie, logique
4 ICJ - Institut Camille Jordan

We construct a bad field in characteristic zero. That is, we construct an algebraically closed field which carries a notion of dimension analogous to Zariski-dimension, with an infinite proper multiplicative subgroup of dimension one, and such that the field itself has dimension two. This answers a longstanding open question by Zilber.

Mots clés: bad fields; amalgamation construction; collaps; green field

Domaines: Logique [math.LO]

Andreas Baudisch, Martin Hils, Amador Martin-Pizarro, Frank Olaf Wagner. Die böse Farbe. Journal of the Institute of Mathematics of Jussieu, 2009, 8 (3), pp.415-443. ⟨10.1017/S1474748008000091⟩. ⟨hal-00863724⟩