The tom Dieck splitting theorem in equivariant motivic homotopy theory

TL;DR

This paper extends the classical tom Dieck splitting theorem to equivariant motivic homotopy theory, providing new structural tools like geometric fixed point functors and the motivic Adams isomorphism.

Contribution

It introduces a version of the tom Dieck splitting theorem within equivariant motivic homotopy theory and develops foundational structures such as geometric fixed points and the motivic Adams isomorphism.

Findings

Established a motivic version of the tom Dieck splitting theorem.

Developed geometric fixed point functors for equivariant motivic spectra.

Proved the motivic Adams isomorphism in this setting.

Abstract

We establish, in the setting of equivariant motivic homotopy theory for a finite group, a version of tom Dieck's splitting theorem for the fixed points of a suspension spectrum. Along the way we establish structural results and constructions for equivariant motivic homotopy theory of independent interest. This includes geometric fixed point functors and the motivic Adams isomorphism.