The Motivic Hopf Map Solves the Homotopy Limit Problem for $K$-Theory

Oliver Röndigs; Markus Spitzweck; Paul Arne Østvær

doi:10.4171/dm/650

JournalsdmVol. 23pp. 1405–1424

The Motivic Hopf Map Solves the Homotopy Limit Problem for $K$ -Theory

Oliver Röndigs
Mathematisches Institut, Universität Osnabrück, Germany
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Markus Spitzweck
Mathematisches Institut, Universität Osnabrück, Germany
- zbMATH Open
Paul Arne Østvær
Department of Mathematics, University of Oslo, Norway

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Abstract

We solve affirmatively the homotopy limit problem for (effective) $K$ -theory over fields of finite virtual cohomological dimension. Our solution uses the motivic slice filtration and the first motivic Hopf map.

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Oliver Röndigs, Markus Spitzweck, Paul Arne Østvær, The Motivic Hopf Map Solves the Homotopy Limit Problem for $K$ -Theory. Doc. Math. 23 (2018), pp. 1405–1424

DOI 10.4171/DM/650