E-motives and motivic stable homotopy

Original · EN

We introduce in this work the notion of the category of pure E-Motives, where E is a motivic strict ring spectrum and construct twisted E-cohomology by using six functors formalism of J. Ayoub. In particular, we construct the category of pure Chow-Witt motives CHW(k)Q over a field k and show that this category admits a fully faithful embedding into the geometric stable A¹-derived category DA¹,gm(k)Q.