# Perfection in motivic homotopy theory

## TL;DR

This paper establishes a topological invariance property for the motivic homotopy category after inverting certain characteristics, leading to new duality results in motivic homotopy theory.

## Contribution

It proves a topological invariance for the motivic homotopy category up to inverting exponential characteristics, and applies this to establish Grothendieck-Verdier duality.

## Key findings

- Invariance of SH[1/p] under passing to perfections for characteristic p schemes
- Proof of Grothendieck-Verdier duality in motivic homotopy context
- Topological invariance holds after inverting exponential characteristics

## Abstract

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 SH[1/p] of characteristic p>0 schemes is invariant under passing to perfections. Among other applications we prove Grothendieck-Verdier duality in this context.