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The Morel-Voevodsky localization theorem in spectral algebraic geometry. (English) Zbl 1451.14068
Summary: 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 \(\mathbf{A}^1\)-homotopy-invariance kills all higher homotopy groups of a connective commutative ring spectrum.

14F42 Motivic cohomology; motivic homotopy theory
14A30 Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.)
14F08 Derived categories of sheaves, dg categories, and related constructions in algebraic geometry
55P43 Spectra with additional structure (\(E_\infty\), \(A_\infty\), ring spectra, etc.)
55P42 Stable homotopy theory, spectra
Full Text: DOI
[1] 10.2140/gt.2014.18.1149 · Zbl 1308.14021
[2] 10.1215/00127094-0000014X · Zbl 1401.14118
[3] 10.4310/PAMQ.2014.v10.n1.a2 · Zbl 1327.14013
[4] ; Grothendieck, Inst. Hautes √Čtudes Sci. Publ. Math., 32, 5 (1967)
[5] 10.2140/agt.2014.14.3603 · Zbl 1351.14013
[6] 10.1016/j.aim.2016.09.031 · Zbl 1400.14065
[7] 10.1007/BFb0059750 · Zbl 0221.14001
[8] 10.1515/9781400830558 · Zbl 1175.18001
[9] 10.1007/BF02698831 · Zbl 0983.14007
[10] 10.1016/j.aim.2014.10.011 · Zbl 1315.14030
[11] 10.1090/memo/0902 · Zbl 1145.14003
[12] 10.1016/j.jpaa.2009.11.004 · Zbl 1194.55020
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