Zilber's notion of logically perfect structure: Universal Covers
arXiv:2302.04650 · doi:10.2140/mt.2024.3.647
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.
1 figure Accepted for publication (October 2023) by the journal Model Theory