Strongly minimal groups in o-minimal structures

Pantelis E Eleftheriou, Assaf Hasson, Ya'acov Peterzil

Research output: Contribution to journalArticlepeer-review

Abstract

We prove Zilber’s Trichotomy Conjecture for strongly minimal expansions of 2-dimensional groups, definable in o-minimal structures:
Theorem. Let M be an o-minimal expansion of a real closed field, hGI Ci a 2-dimensional group definable in M, and D D hGI C; : : :i 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
Original languageEnglish GB
Pages (from-to)3351-3418
Number of pages68
JournalJournal of the European Mathematical Society
Volume23
Issue number10
StatePublished - 2021

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