JournalsjemsVol. 14, No. 4pp. 1041–1079

Algebraic KK-theory of the first Morava KK-theory

  • John Rognes

    University of Oslo, Norway
  • Christian Ausoni

    Universität Münster, Germany
Algebraic $K$-theory of the first Morava $K$-theory cover
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Abstract

For a prime p5p \ge 5, we compute the algebraic KK-theory modulo pp and v1v_1 of the mod pp Adams summand, using topological cyclic homology. On the way, we evaluate its modulo pp and v1v_1 topological Hochschild homology. Using a localization sequence, we also compute the KK-theory modulo pp and v1v_1 of the first Morava KK-theory.

Cite this article

John Rognes, Christian Ausoni, Algebraic KK-theory of the first Morava KK-theory. J. Eur. Math. Soc. 14 (2012), no. 4, pp. 1041–1079

DOI 10.4171/JEMS/326