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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Zilber’s restricted trichotomy in characteristic zero
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by Benjamin Castle
J. Amer. Math. Soc.
Published electronically: October 3, 2023


We prove the characteristic zero case of Zilber’s Restricted Trichotomy Conjecture. That is, we show that if $\mathcal M$ is any non-locally modular strongly minimal structure interpreted in an algebraically closed field $K$ of characteristic zero, then $\mathcal M$ itself interprets $K$; in particular, any non-1-based structure interpreted in $K$ is mutually interpretable with $K$. Notably, we treat both the ‘one-dimensional’ and ‘higher-dimensional’ cases of the conjecture, introducing new tools to resolve the higher-dimensional case and then using the same tools to recover the previously known one-dimensional case.
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Bibliographic Information
  • Benjamin Castle
  • Affiliation: Department of mathematics, Ben Gurion University of the Negev, Be’er Sehva, Israel
  • ORCID: 0000-0002-6006-1329
  • Email:
  • Received by editor(s): November 22, 2022
  • Received by editor(s) in revised form: June 12, 2023
  • Published electronically: October 3, 2023
  • Additional Notes: This work was partially supported by the Field Institute for Research in Mathematical Sciences, and by NSF Grant DMS #1800692
  • © Copyright 2023 American Mathematical Society
  • Journal: J. Amer. Math. Soc.
  • MSC (2020): Primary 03C45; Secondary 14A99
  • DOI: