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Morava K-theory of orthogonal groups and motives of projective quadrics

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arxiv 2011.14720 v3 pith:UZOOMVBR submitted 2020-11-30 math.KT

Nikita Geldhauser , Andrei Lavrenov , Victor Petrov , Pavel Sechin This is my paper · ORCID
classification math.KT
keywords moravaorthogonalgroupsk-theorymotivesresultsspecialspin
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We compute the algebraic Morava K-theory ring of split special orthogonal and spin groups. In particular, we establish certain stabilization results for the Morava K-theory of special orthogonal and spin groups. Besides, we apply these results to study Morava motivic decompositions of orthogonal Grassmannians. For instance, we determine all indecomposable summands of the Morava motives of a generic quadric.

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