Model theory of proalgebraic groups

Michael Wibmer, Anand Pillay

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)2225-2267
Number of pages43
JournalTransactions of the American Mathematical Society
Volume374
Issue number3
Early online date2020
DOIs
Publication statusPublished - Mar 2021

Keywords

  • Affine group schemes
  • Proalgebraic groups
  • Representation theory
  • Tannakian categories

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics(all)

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