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The generalized slices of Hermitian \(K\)-theory. (English) Zbl 1453.14065
Summary: We compute the generalized slices (as defined by Spitzweck-Østvær) 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.

MSC:
14F42 Motivic cohomology; motivic homotopy theory
19E08 \(K\)-theory of schemes
55P42 Stable homotopy theory, spectra
14C25 Algebraic cycles
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