TL;DR
This paper investigates the self-duality properties of Grothendieck's blended extensions within tannakian categories, providing a torsor framework to analyze their monodromy groups and unipotent radicals.
Contribution
It introduces a torsor structure on symmetric and antisymmetric blended extensions, facilitating the computation of monodromy group radicals in new contexts.
Findings
Torsor structure on blended extensions established
Method to compute unipotent radicals of monodromy groups
Applications to various tannakian categories
Abstract
We study self-duality of Grothendieck's blended extensions (extensions panach\'ees) in the context of a tannakian category. The set of equivalence classes of symmetric, resp. antisymmetric, blended extensions is naturally endowed with a torsor structure, which enables us to compute the unipotent radical of the associated monodromy groups in various situations
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