Submission date: 9 February 2023

Abstract:

We sketch recent interactions between model theory and a roughly 150-year old study of analytic functions involving complex analysis, algebraic topology, and number theory, centered in canonicity of universal covers. Towards this goal we discuss in a systematic and unified way several examples indicating the main ideas of the proofs and the necessary changes in method for different situations: exponential covers, modular and Shimura curves, Shimura and abelian varieties, and coherent families of smooth covers.

Mathematics Subject Classification: 03C45, 03C64, 03C98, 11U09, 12L12, 03-03, 03C75, 03C48

Keywords and phrases:

Full text arXiv 2302.04650: pdf, ps.