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Model theory and the Tannakian formalism


Author: Moshe Kamensky
Journal: Trans. Amer. Math. Soc. 367 (2015), 1095-1120
MSC (2010): Primary 03C40, 14L17, 18D10, 20G05
Published electronically: October 10, 2014
MathSciNet review: 3280038
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Abstract: We draw the connection between the model theoretic notions of internality and the binding group on one hand, and the Tannakian formalism on the other.

More precisely, we deduce the fundamental results of the Tannakian formalism by associating to a Tannakian category a first order theory, and applying the results on internality there. We then formulate the notion of a differential tensor category, which axiomatises the category of differential representations of differential linear groups, and show how the model theoretic techniques can be used to deduce the analogous results in that context.


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Additional Information

Moshe Kamensky
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Address at time of publication: Department of Mathematics, Ben-Gurion University, Be’er-Sheva, Israel
Email: kamensky.1@nd.edu, kamenskm@math.bgu.ac.il

DOI: https://doi.org/10.1090/S0002-9947-2014-06062-5
Keywords: Internality, binding group, Galois group, Tannakian formalism, linear algebraic group, linear differential group, representations
Received by editor(s): October 10, 2010
Received by editor(s) in revised form: December 20, 2012
Published electronically: October 10, 2014
Article copyright: © Copyright 2014 American Mathematical Society