Abstract
Zariski groups are ℵ0-stable groups with an axiomatically given Zariski topology and thus abstract generalizations of algebraic groups. A large part of algebraic geometry can be developed for Zariski groups. As a main result, any simple smooth Zariski group interprets an algebraically closed field, hence is almost an algebraic group over an algebraically closed field.
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Junker, M. Completeness in Zariski groups. Isr. J. Math. 109, 273–298 (1999). https://doi.org/10.1007/BF02775039
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DOI: https://doi.org/10.1007/BF02775039