Operads and Γ-homology of commutative rings

Abstract

We introduce Γ-homology, the natural homology theory for E ∞ -algebras, and a cyclic version of it. Γ-homology specializes to a new homology theory for discrete commutative rings, very different in general from André–Quillen homology. We prove its general properties, including at base change and transitivity theorems. We give an explicit bicomplex for the Γ-homology of a discrete algebra, and elucidate connections with stable homotopy theory.