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.


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