The Generalized Slices of Hermitian K-Theory

TL;DR

This paper computes the generalized slices of the motivic spectrum KO, representing hermitian K-theory, linking it to motivic cohomology and confirming predictions from classical topology and conjectures in motivic homotopy theory.

Contribution

It provides explicit calculations of the generalized slices of hermitian K-theory spectrum KO in the motivic setting, connecting them to motivic cohomology and advancing understanding of motivic homotopy sheaves.

Findings

Computed generalized slices of KO spectrum in motivic homotopy theory.

Established a version of Morel's conjecture on homotopy sheaves of generalized motivic cohomology.

Confirmed agreement with classical topology and theoretical predictions.

Abstract

We compute the generalized slices (as defined by Spitzweck-{\O}stv{\ae}r) of the motivic spectrum KO (representing hermitian K-theory) in terms of motivic cohomology and (a version of) generalized motivic cohomology, obtaining good agreement with the situation in classical topology and the results predicted by Markett-Schlichting. As an application, we compute the homotopy sheaves of (this version of) generalized motivic cohomology, which establishes a version of a conjecture of Morel.