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arXiv · 2405.01399

Algebraic types in Zilber's exponential field

Vahagn Aslanyan·Jonathan Kirby
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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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Vahagn Aslanyan, Jonathan Kirby. 2024-05-02. Algebraic types in Zilber's exponential field. https://doi.org/10.2140/mt.2025.4.37

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