2018/10/03 by Eleftheriou, Pantelis, Hasson, Assaf, Peterzil, Ya'acov
#03C45 #03C64 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1810.01650
We prove Zilber's Trichotomy Conjecture for strongly minimal expansions of two-dimensional groups, definable in o-minimal structures: Theorem. Let M be an o-minimal expansion of a real closed field, (G;+) a 2-dimensional group definable in M, and D = (G;+,...) a strongly minimal structure, all of whose atomic relations are definable in M. If D is not locally modular, then an algebraically closed field K is interpretable in D, and the group G, with all its induced D-structure, is definably isomorphic in D to an algebraic K-group with all its induced K-structure.