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Preprint Number 2350
2350. Ugur Efem, Boris Zilber On the Theory of Specialisations of Regular Covers of Zariski Structures Authors: Ugur Efem, Boris Zilber E-mail: Submission date: 16 February 2023 Abstract: In algebraic geometry specialisations and valuations play and important role. In this paper we start investigating analogous structures for Zariski structures. Specifically, we look into the existence and uniqueness properties of extensions of universal specialisations from a base Zariski structure to its regular cover. In the process we begin to uncover some structural properties of regular covers of Zariski structures, and also to uncover the type of topological properties necessary for a Zariski structure to have a good theory of specialisations. A subclass of Zariski structures is identified with a good theory of specialisations. Mathematics Subject Classification: Primary: 03C07, 03C10, 03C35, 03C50, 03C52, Secondary: 14A99, 18F15, 55R65, 57R22 Keywords and phrases: Full text
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