Motivic spectra and universality of $K$-theory

Abstract

We develop a theory of motivic spectra in a broad generality; in particular ${\mathbb{A}}^1$-homotopy invariance is not assumed. As an application, we prove that $K$-theory of schemes is a universal Zariski sheaf of spectra which is equipped with an action of the Picard stack and satisfies projective bundle formula.

v3: 47 pages, small corrections and edits, the numbering has not been changed from v2