Motifs généralisées et orientations symplectiques

Abstract : In this thesis, we present a general framework to construct categories of motives and build part of the six operations formalism for these categories. In the case of MW-motivic cohomology, we prove the quaternionic projective bundle theorem and construct a Gysin triangle, which enable us to define Pontryagin classes on Chow-Witt rings for symplectic bundles. Applying these tools together, we compute the group of morphisms between smooth proper schemes in the category of (effective) MW-motives.
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Nanjun Yang. Motifs généralisées et orientations symplectiques. Topologie géométrique [math.GT]. Université Grenoble Alpes, 2019. Français. ⟨NNT : 2019GREAM004⟩. ⟨tel-02191436⟩

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