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.
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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