Connective KK-theory and Adams operations

  • Olivier Haution

    Ludwig-Maximilians-Universität München, Germany
  • Alexander Merkurjev

    University of California, Los Angeles, USA
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We investigate the relations between the Grothendieck group of coherent modules of an algebraic variety and its Chow group of algebraic cycles modulo rational equivalence. Those are in essence torsion phenomena, which we attempt to control by considering the action of the Adams operations on the Brown–Gersten–Quillen spectral sequence and related objects, such as connective K0K_0-theory. We provide elementary arguments whenever possible. As applications, we compute the connective K0K_0-theory of the following objects: (1) the variety of reduced norm one elements in a central division algebra of prime degree; (2) the classifying space of the split special orthogonal group of odd degree.

Cite this article

Olivier Haution, Alexander Merkurjev, Connective KK-theory and Adams operations. EMS Surv. Math. Sci. 8 (2021), no. 1/2, pp. 135–162

DOI 10.4171/EMSS/50