Model theory of proalgebraic groups

Model theory of proalgebraic groups

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 clas...

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Veröffentlicht in:Transactions of the American Mathematical Society 2021-03, Vol.374 (3), p.2225-2267
Hauptverfasser: Pillay, Anand, Wibmer, Michael
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description 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.
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