ELLIPTIC COHOMOLOGY IS UNIQUE UP TO HOMOTOPY

Abstract

Abstract Homotopy theory folklore tells us that the sheaf defining the cohomology theory $\operatorname {\mathrm {Tmf}}$ of topological modular forms is unique up to homotopy. Here we provide a proof of this fact, although we claim no originality for the statement. This retroactively reconciles all previous constructions of $\operatorname {\mathrm {Tmf}}$ .