Algebraic types in Zilber's exponential field

Aslanyan, Vahagn and Kirby, Jonathan (2025) Algebraic types in Zilber's exponential field. Model Theory, 4 (1). pp. 37-58. ISSN 2832-904X

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Abstract

We characterise the model-theoretic algebraic closure in Zilber's exponential field. A key step involves showing that certain algebraic varieties have finite intersections with certain finite-rank subgroups of the graph of exponentiation. Mordell-Lang for algebraic tori (a theorem of Laurent) plays a central role in our proof.

Item Type:	Article
Additional Information:	Funding information: Most of this work was done while Aslanyan was a senior research associate at the University of East Anglia, where both authors were supported by EPSRC grant EP/S017313/1. Aslanyan has continued to work on this paper at the University of Leeds (supported by Leverhulme Trust Early Career Fellowship ECF-2022-082) and at the University of Manchester (supported by EPSRC Open Fellowship EP/X009823/1). Rights Retention Statement: For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising from this submission
Uncontrolled Keywords:	math.lo,math.nt,03c60 (primary), 03c65, 12l12
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024) Faculty of Science > School of Engineering, Mathematics and Physics
UEA Research Groups:	Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR) Faculty of Science > Research Groups > Logic (former - to 2024)
Related URLs:	http://arxiv.org/pdf/2405.01399v2
Depositing User:	LivePure Connector
Date Deposited:	27 Nov 2024 10:47
Last Modified:	06 Feb 2025 12:27
URI:	https://ueaeprints.uea.ac.uk/id/eprint/97783
DOI:	10.2140/mt.2025.4.37

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