Strongly minimal groups in o-minimal structures
Logic
2021-04-13 v3
Abstract
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.
Cite
@article{arxiv.1810.01650,
title = {Strongly minimal groups in o-minimal structures},
author = {Pantelis Eleftheriou and Assaf Hasson and Ya'acov Peterzil},
journal= {arXiv preprint arXiv:1810.01650},
year = {2021}
}