On voevodsky's algebraic k-theory spectrum

Abstract

Under a certain normalization assumption we prove that the P1 -spectrum BGL of Voevodsky which represents algebraic K-theory is unique over Spec(ℤ). Following an idea of Voevodsky, we equip the P1 -spectrum BGL with the structure of a commutative P1-ring spectrum in the motivic stable homotopy category. Furthermore, we prove that under a certain normalization assumption this ring structure is unique over Spec(ℤ). For an arbitrary Noetherian scheme S of finite Krull dimension we pull this structure back to obtain a distinguished monoidal structure on BGL. This monoidal structure is relevant for our proof of the motivic Conner-Floyd theorem (Panin et al., Invent Math 175: 435-451, 2008). It has also been used to obtain a motivic version of Snaith's theorem (Gepner and Snaith, arXiv:0712.2817v1 [math.AG]). © Springer-Verlag Berlin Heidelberg 2009.