Corrigendum: Uniqueness of smooth extensions of generalized cohomology theories

TL;DR

This paper corrects and strengthens the proof of a key theorem regarding the flat part of differential extensions of generalized cohomology theories, ensuring the validity of prior results and providing more robust conclusions.

Contribution

It provides a correct proof of the flat part identification and extends some results from the original work on smooth cohomology theories.

Findings

Corrected proof of Theorem 7.12

Stronger versions of previous results

Validation of the flat part as ER/Z

Abstract

The proof of Theorem 7.12 of "Uniqueness of smooth cohomology theories" by the authors of this note is not correct. The said theorem identifies the flat part of a differential extension of a generalized cohomology theory E with ER/Z (there called "smooth extension"). In this note, we give a correct proof. Moreover, we prove slightly stronger versions of some of the other results of that paper.