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arXiv · 2302.04650

Zilber's notion of logically perfect structure: Universal Covers

John T. Baldwin·Andrés Villaveces
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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.

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John T. Baldwin, Andrés Villaveces. 2023-02-09. Zilber's notion of logically perfect structure: Universal Covers. https://doi.org/10.2140/mt.2024.3.647

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