Ind‐étale versus formally étale

Abstract We show that when is a reduced algebra over a characteristic zero field and the module of Kähler differentials , then is ind‐étale, partially answering a question of Bhatt. As further applications of this result, we deduce a rigidity property of Hochschild homology and special instances of Weibel's conjecture and Vorst's conjecture without any noetherian assumptions.