Original version
Mathematische Zeitschrift. 2020, 294 (3-4), 1021-1034, DOI: https://doi.org/10.1007/s00209-019-02302-z
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.