Perfection in motivic homotopy theory.(English)Zbl 1440.14123

Summary: We prove a topological invariance statement for the Morel-Voevodsky motivic homotopy category up to inverting exponential characteristics of residue fields. This implies in particular that $$\mathbf{SH} \left[\frac{1}{p}\right]$$ of characteristic $$p > 0$$ schemes is invariant under passing to perfections. Among other applications, we prove Grothendieck-Verdier duality in this context.

MSC:

 14F42 Motivic cohomology; motivic homotopy theory 19E08 $$K$$-theory of schemes 19E15 Algebraic cycles and motivic cohomology ($$K$$-theoretic aspects)
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