Submission date: 27 August 2019

Abstract:

We lay the foundations for a model theoretic study of proalgebraic groups. Our axiomatization is based on the tannakian philosophy. Through a tensor analog of skeletal categories we are able to consider neutral tannakian categories with a fibre functor as many-sorted first order structures. The class of diagonalizable proalgebraic groups is analyzed in detail. We show that the theory of a diagonalizable proalgebraic group G is determined by the theory of the base field and the theory of the character group of G. Some initial steps towards a comprehensive study of types are also made.

Mathematics Subject Classification: 03C60, 03C65, 14L15, 14L17, 20G05, 18D10

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Full text arXiv 1908.10064: pdf, ps.