Scalar Extension of Abelian and Tannakian Categories

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dc.creatorStalder, Nicolas
dc.date2008-06-02
dc.date.accessioned2026-07-07T09:42:14Z
dc.date.available2026-07-07T09:42:14Z
dc.descriptionWe introduce and develop the notion of scalar extension for abelian categories. Given a field extension F'/F, to every F-linear abelian category A satisfying a suitable finiteness condition we associate an F'-linear abelian category A' and an exact F-linear functor t: A --> A'. This functor is universal among F-linear right exact functors with target an F'-linear abelian category. We discuss various basic properties of this concept, among others compatibilities with multilinear endofunctors such as tensor products, and the permanence of favourable properties of the functors and categories involved. We obtain the notion of scalar extension for Tannakian categories, which allows us to deduce consequences for the algebraic monodromy groups of Tannakian categories.
dc.description37 pages
dc.identifierhttps://arxiv.org/abs/0806.0308
dc.identifierhttp://arxiv.org/abs/0806.0308
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/162106
dc.subjectCategory Theory
dc.subjectAlgebraic Geometry
dc.subject18E10; 14F42
dc.titleScalar Extension of Abelian and Tannakian Categories
dc.typetext

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