Quaternionic projective bundle theorem and Gysin triangle in MW-motivic cohomology

Abstract

In this paper, we show that the motive of the quaternionic Grassmannian \(HP^n\) (as defined by I. Panin and C. Walter) splits in the category of effective MW-motives (as defined by B. Calmès, F. Déglise and J. Fasel). 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.

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Acknowledgements

The author would like to thank his PhD advisor J. Fasel for giving me the basic idea of this article and helping during the subsequent research, and F. Déglise for helpful discussions. The careful work of the referee is also greatly appreciated.

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Correspondence to Nanjun Yang.

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Yang, N. Quaternionic projective bundle theorem and Gysin triangle in MW-motivic cohomology. manuscripta math. 164, 39–65 (2021). https://doi.org/10.1007/s00229-019-01171-4

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Mathematics Subject Classification

  • Primary: 11E81
  • 14F42