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.

27 pages, minor revisions; to appear in Geometry & Topology

References in corpus (2)

• Higher Topos Theory
• A^1-homotopy invariance in spectral algebraic geometry

Cited by in corpus (7)

• Virtual fundamental classes of derived stacks I
• K-theory and G-theory of derived algebraic stacks
• Algebraic K-theory of quasi-smooth blow-ups and cdh descent
• The intrinsic stable normal cone
• Categorical Milnor squares and K-theory of algebraic stacks
• A^1-homotopy invariance in spectral algebraic geometry
• A categorification of the quantum Lefschetz principle