The completion and local cohomology theorems for complex cobordism for all compact Lie groups

TL;DR

This paper extends the completion and local cohomology theorems for complex cobordism to all compact Lie groups, confirming a conjecture and broadening the scope of equivariant stable homotopy theory.

Contribution

It generalizes the completion theorem for equivariant MU-module spectra from finite groups to all compact Lie groups, utilizing Schwede's splitting of global functors.

Findings

Proves the completion theorem for all compact Lie groups.

Confirms a conjecture of Greenlees and May.

Extends the applicability of equivariant MU-module spectra.

Abstract

We generalize the completion theorem for equivariant MU-module spectra for finite groups or finite extensions of a torus to compact Lie groups using the splitting of global functors proved by Schwede. This proves a conjecture of Greenlees and May.