Strongly minimal groups in o-minimal structures

  • Pantelis E. Eleftheriou

    University of Konstanz, Germany
  • Assaf Hasson

    Ben Gurion University of the Negev, Be’er-Sheva, Israel
  • Ya'acov Peterzil

    University of Haifa, Israel
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Abstract

We prove Zilber’s Trichotomy Conjecture for strongly minimal expansions of 2-dimensional groups, definable in o-minimal structures:

Theorem. Let be an o-minimal expansion of a real closed field, a 2-dimensional group definable in , and a strongly minimal structure, all of whose atomic relations are definable in . If is not locally modular, then an algebraically closed field is interpretable in , and the group , with all its induced -structure, is definably isomorphic in to an algebraic -group with all its induced -structure.

Cite this article

Pantelis E. Eleftheriou, Assaf Hasson, Ya'acov Peterzil, Strongly minimal groups in o-minimal structures. J. Eur. Math. Soc. 23 (2021), no. 10, pp. 3351–3418

DOI 10.4171/JEMS/1095