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.

On very effective hermitian K-theory / A. Ananyevskiy, O. Rondigs, P.A. Oestvaer. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 294:3-4(2020), pp. 1021-1034. [10.1007/s00209-019-02302-z]

On very effective hermitian K-theory

P.A. Oestvaer
2020

Abstract

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.
A1-homotopy theory; Hermitian K-theory; Slice filtration
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/860090
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