Operations on Milnor–Witt K-theory

For all integers $n$ and all homotopy modules $M_{*}$ , we define certain operations ${\underline{K}}_{n}^{MW} \to M_{*}$ and show that these generate the $M_{*} (k)$ -module of all (in general nonadditive) operations ${\underline{K}}_{n}^{MW} \to M_{*}$ in a suitable sense, if $M_{*}$ is $ℕ$ -graded and has a ring structure. This also allows us to explicitly compute the abelian group $Hom ({\underline{K}}_{n}^{MW}, {\underline{K}}_{m}^{MW})$ and all operations between related theories such as Milnor, Witt and Milnor–Witt K-theory.

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Keywords

Milnor K-theory, Milnor–Witt K-theory, homotopy modules, operations, motivic homotopy theory

Mathematical Subject Classification

Primary: 19D45, 55S25

Secondary: 14F42, 55Q35, 55Q45

Milestones

Received: 3 August 2023

Revised: 27 November 2024

Accepted: 23 December 2024

Published: 25 February 2025

Authors

Thor Wittich
Institut für Mathematik Universität Osnabrück Osnabrück Germany

Vol. 10, No. 1, 2025

Thor Wittich

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors