Algebraic types in Zilber's exponential field

Vahagn Aslanyan; Jonathan Kirby

doi:10.2140/mt.2025.4.37

Algebraic types in Zilber's exponential field

Vahagn Aslanyan, Jonathan Kirby

Research output: Contribution to journal › Article › peer-review

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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.

Original language	English
Pages (from-to)	37-58
Number of pages	22
Journal	Model Theory
Volume	4
Issue number	1
DOIs	https://doi.org/10.2140/mt.2025.4.37
Publication status	Published - Jan 2025

Keywords

math.LO
math.NT
03C60 (primary), 03C65, 12L12

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10.2140/mt.2025.4.37

2405.01399v2Accepted author manuscript, 230 KB

http://arxiv.org/pdf/2405.01399v2

Exponentially Algebraically closed fields.
Kirby, J.
Engineering and Physical Sciences Research Council
1/09/19 → 31/08/22
Project: Research

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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. ",

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Algebraic types in Zilber's exponential field

Abstract

Keywords

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Projects

Exponentially Algebraically closed fields.

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