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UNIVERSAL COVERS OF COMMUTATIVE FINITE MORLEY RANK GROUPS

Part of: Abelian varieties and schemes Model theory

Published online by Cambridge University Press:  26 April 2018

Martin Bays ,
Bradd Hart  and
Anand Pillay
Martin Bays
Affiliation:
Institut für Mathematische Logik und Grundlagenforschung, Fachbereich Mathematik und Informatik Universität Münster, Einsteinstrasse 62, 48149 Münster, Germany (mbays@sdf.org)
Bradd Hart
Affiliation:
Department of Mathematics and Statistics McMaster University, 1280 Main St., Hamilton, ON L8S 4K1, Canada (hartb@mcmaster.ca)
Anand Pillay
Affiliation:
Department of Mathematics, University of Notre Dame, 281 Hurley Hall, Notre Dame, IN 46556, USA (apillay@nd.edu)
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Abstract

We give an algebraic description of the structure of the analytic universal cover of a complex abelian variety which suffices to determine the structure up to isomorphism. More generally, we classify the models of theories of ‘universal covers’ of rigid divisible commutative finite Morley rank groups.

Keywords

Abelian varietiesexponential mapKummer theorycategoricityMorley rank

MSC classification

Primary: 03C45: Classification theory, stability and related concepts 03C60: Model-theoretic algebra 14K99: None of the above, but in this section

Information

Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 19 , Issue 3 , May 2020 , pp. 767 - 799
Copyright
© Cambridge University Press 2018

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