Motivic stable homotopy theory is strictly commutative at the characteristic

TL;DR

This paper demonstrates that in the p-local motivic stable category over an Fp-scheme, the mapping spaces inherently possess strictly commutative monoid structures, establishing a canonical form for HZ-modules.

Contribution

It proves that mapping spaces in the motivic stable category are strictly commutative monoids, a novel structural insight in motivic homotopy theory.

Findings

Mapping spaces are strictly commutative monoids.

HZ-modules have canonical structures.

Results apply to p-local motivic categories over Fp-schemes.

Abstract

We show that mapping spaces in the p-local motivic stable category over an Fp-scheme are strictly commutative monoids (whence HZ-modules) in a canonical way.