Model theory of proalgebraic groups

Pillay, Anand; Wibmer, Michael

doi:10.1090/tran/8304

Model theory of proalgebraic groups
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by Anand Pillay and Michael Wibmer PDF

Trans. Amer. Math. Soc. 374 (2021), 2225-2267 Request permission

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.

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