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
Markus Spitzweck
Mathematisches Institut, Universität Osnabrück, Germany
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.

Cite this article

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