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
Original language | English |
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Pages (from-to) | 2225-2267 |
Number of pages | 43 |
Journal | Transactions of the American Mathematical Society |
Volume | 374 |
Issue number | 3 |
Early online date | 2020 |
DOIs | |
Publication status | Published - Mar 2021 |
Keywords
- Affine group schemes
- Proalgebraic groups
- Representation theory
- Tannakian categories
ASJC Scopus subject areas
- Applied Mathematics
- General Mathematics