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

Geldhauser, Nikita; Lavrenov, Andrei; Petrov, Victor und Sechin, Pavel (2024): Morava K-theory of orthogonal groups and motives of projective quadrics. In: Advances in Mathematics, Vol. 446, 109657

Abstract

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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 00018708
• Language: English