#### Volume 23, issue 7 (2019)

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The Morel–Voevodsky localization theorem in spectral algebraic geometry

Geometry & Topology 23 (2019) 3647–3685
##### 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.

##### Keywords
motivic homotopy theory, derived algebraic geometry, commutative ring spectra
##### Mathematical Subject Classification 2010
Primary: 14F05, 14F42, 55P43
Secondary: 55P42