-theory as an Eilenberg-Mac Lane spectrum

  • D. Kaledin


For an additive Waldhausen category linear over a ring , the corresponding -theory spectrum is a module spectrum over the -theory spectrum of . Thus if is a finite field of characteristic , then after localization at , we obtain an Eilenberg-MacLane spectrum -- in other words, a chain complex. We propose an elementary and direct construction of this chain complex that behaves well in families and uses only methods of homological algebra (in particular, the notions of a ring spectrum and a module spectrum are not used).