On very effective Hermitian \(K\)-theory. (English) Zbl 1453.14064
Summary: We argue that the very effective cover of hermitian \(K\)-theory in the sense of motivic homotopy theory is a convenient algebro-geometric generalization of the connective real topological \(K\)-theory spectrum. This means the very effective cover acquires the correct Betti realization, its motivic cohomology has the desired structure as a module over the motivic Steenrod algebra, and that its motivic Adams and slice spectral sequences are amenable to calculations.
MSC:
| 14F42 | Motivic cohomology; motivic homotopy theory |
| 19G38 | Hermitian \(K\)-theory, relations with \(K\)-theory of rings |
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