# The very effective covers of KO and KGL over Dedekind schemes

@inproceedings{Bachmann2022TheVE, title={The very effective covers of KO and KGL over Dedekind schemes}, author={Tom Bachmann}, year={2022} }

We answer a question of Hoyois–Jelisiejew–Nardin–Yakerson regarding framed models of motivic connective K-theory spectra over Dedekind schemes. That is, we show that the framed suspension spectrum of the presheaf of groupoids of vector bundles (respectively non-degenerate symmetric bilinear bundles) is the effective cover of KGL (respectively very effective cover of KO). One consequence is that, over any scheme, we obtain a spectral sequence from Spitzweck’s motivic cohomology to homotopy…

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