The Morel–Voevodsky localization theorem in spectral algebraic geometry

Abstract

We prove an analogue of the Morel–Voevodsky localization theorem over spectral algebraic spaces. As a corollary we deduce a “derived nilpotent-invariance” result which, informally speaking, says that $A^1$–homotopy-invariance kills all higher homotopy groups of a connective commutative ring spectrum.