Quaternionic Projective Bundle Theorem and Gysin Triangle in MW-Motivic Cohomology

Abstract

In this paper, we show that the motive of the quaternionic Grassmannian $H{P}^n$ (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.

Final version, 16 pages, substantially revised, results improved, to appear in Manuscripta Mathematica

Cited by in corpus (3)

• Chow-Witt rings of classifying spaces for symplectic and special linear groups
• Thom isomorphisms in triangulated motivic categories
• Milnor-Witt motivic cohomology of complements of hyperplane arrangements