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Morava $J$-invariant

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arxiv 2409.14099 v1 pith:3WMU4YMQ submitted 2024-09-21 math.KT

Nikita Geldhauser , Andrei Lavrenov , Victor Petrov , Pavel Sechin This is my paper · ORCID
classification math.KT
keywords moravacomputeinvariantk-theoryorthogonalalgebraicallowsanalogue
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abstract

We compute the co-multiplication of the algebraic Morava K-theory for split orthogonal groups. This allows us to compute the decomposition of the Morava motives of generic maximal orthogonal Grassmannians and to compute a Morava K-theory analogue of the $J$-invariant in terms of the ordinary (Chow) $J$-invariant.

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  1. Invertible Morava motives in quadrics

    math.AG 2025-04 conditional novelty 8.0 of 10

    Milnor K-theory modulo 2 embeds into the Picard group of invertible Morava K-theory motives, with quadrics providing the construction and with Chow motives recoverable from Morava motives in the low-dimensional case.

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