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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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