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Quaternionic projective bundle theorem and Gysin triangle in MW-motivic cohomology. (English) Zbl 1466.14025

Summary: In this paper, we show that the motive of the quaternionic Grassmannian \(HP^n\) (as defined by I. Panin and C. Walter [“Quaternionic Grassmannians and Pontryagin classes in algebraic geometry”, Preprint, arXiv:1011.0649]) splits in the category of effective MW-motives (as defined by B. Calmès and J. Fasel [“The category of finite Chow-Witt correspondences”, Preprint, arXiv:1412.2989] and F. Déglise and J. Fasel [“MW-motivic complexes”, Preprint, arXiv:1708.06095]). Moreover, we extend this result to an arbitrary symplectic bundle, obtaining the so-called quaternionic projective bundle theorem. Finally, we give the Gysin triangle in MW-motivic cohomology.

MSC:

14F42 Motivic cohomology; motivic homotopy theory
19E15 Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects)
11E81 Algebraic theory of quadratic forms; Witt groups and rings
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