Preorientations of the derived motivic multiplicative group

Abstract

We provide a proof in the language of model categories and symmetric spectra of Lurie's theorem that topological complex $K$-theory represents orientations of the derived multiplicative group. Then we generalize this result to the motivic situation. Along the way, a number of useful model structures and Quillen adjunctions both in the classical and in the motivic case are established.

erratum added

References in corpus (2)

• Higher Topos Theory
• On a conjecture of Morel

Cited by in corpus (4)

• Triangulated categories of mixed motives
• Arakelov motivic cohomology I
• Motivic twisted K-theory
• Another viewpoint on J-spaces