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Algebraic types in Zilber's exponential field

Logic 2025-01-22 v2 Number Theory

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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Cite

@article{arxiv.2405.01399,
  title  = {Algebraic types in Zilber's exponential field},
  author = {Vahagn Aslanyan and Jonathan Kirby},
  journal= {arXiv preprint arXiv:2405.01399},
  year   = {2025}
}

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Minor revisions

R2 v1 2026-06-28T16:14:16.904Z