On the log motivic stable homotopy groups

TL;DR

This paper demonstrates that the log motivic stable homotopy groups are isomorphic to the classical motivic stable homotopy groups over perfect fields with resolution of singularities, bridging two important homotopy theories.

Contribution

It establishes an isomorphism between log motivic and usual motivic stable homotopy groups over certain fields, clarifying their relationship.

Findings

Log motivic and usual motivic stable homotopy groups are isomorphic.

The comparison holds over perfect fields admitting resolution of singularities.

Provides a foundation for further study of log motivic homotopy theory.

Abstract

We compare the log motivic stable homotopy category and the usual motivic stable homotopy category over a perfect field admitting resolution of singularities. As a consequence, we show that the log motivic stable homotopy groups are isomorphic to the usual motivic stable homotopy groups.