Submission date: 2 May 2024

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.

Mathematics Subject Classification: 03C60 (primary), 03C65, 12L12

Keywords and phrases:

Full text arXiv 2405.01399: pdf, ps.