The localization theorem for framed motivic spaces

TL;DR

This paper establishes a localization theorem for framed motivic spaces, showing their equivalence to motivic spectra over schemes and providing a new way to construct motivic cohomology for arbitrary schemes.

Contribution

It proves a localization theorem for framed motivic spaces and introduces a novel construction of motivic cohomology applicable to all schemes.

Findings

Framed motivic spectra are equivalent to motivic spectra over any scheme.

A new construction method for motivic cohomology of arbitrary schemes.

Extension of the Morel-Voevodsky localization theorem to framed motivic spaces.

Abstract

We prove the analog of the Morel-Voevodsky localization theorem for framed motivic spaces. We deduce that framed motivic spectra are equivalent to motivic spectra over arbitrary schemes, and we give a new construction of the motivic cohomology of arbitrary schemes.