Motivic strict ring models for 𝐾-theory

Abstract

It is shown that the K K -theory of every noetherian base scheme of finite Krull dimension is represented by a commutative strict ring object in the setting of motivic stable homotopy theory. The adjective ‘strict’ is used here in order to distinguish between the type of ring structure we construct and one which is valid only up to homotopy. An analogous topological result follows by running the same type of arguments as in the motivic setting.