The very effective covers of KO and KGL over Dedekind schemes

  • Tom Bachmann

    Ludwig-Maximilians-Universität München, Germany; University of Oslo, Norway; Johannes Gutenberg-Universität Mainz, Germany
The very effective covers of KO and KGL over Dedekind schemes cover

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Abstract

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

Cite this article

Tom Bachmann, The very effective covers of KO and KGL over Dedekind schemes. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1458