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Theses

Une étude modèle-théorique du formalisme tannakien

Abstract : In this thesis, we define and study a formalism which allows one to work on Tannakian questions for groups defined over generalized differential rings, which generalize both differential rings and difference rings. We define a notion of differential Tanakian category which is similar to the usual Tannakian formalism, adding a structure which permits to describe the differential structure induced by the generalized differential. We then study the model-theoretical properties of the resulting categories, realizing the Tannakian group associated to a category as a model-theoretical binding group. In the last chapter, we study the notion of universe associated to a first-order structure, and we introduce a topology in this context, which is reminiscent of the topology on the spaces of types in first-order Model Theory. We also study the notion of binding groupoid from the point of view of universes
Keywords : Tannakian formalism
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Simon Iosti. Une étude modèle-théorique du formalisme tannakien. Anneaux et algèbres [math.RA]. Université Claude Bernard - Lyon I, 2014. Français. ⟨NNT : 2014LYO10106⟩. ⟨tel-01806161⟩

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