Abstract: The classical Hochschild–Kostant–Rosenberg theorem identifies Hochschild homology of a commutative ring which is smooth over the base field with its de Rham complex. In this talk, we provide a generalisation to topological Hochschild homology of commutative ring spectra, replacing the de Rham complex by an “$$\eta$$-deformed de Rham complex” which incorporates the $$E_\infty$$ structure. Joint with Thomas Nikolaus.