# Rigidity in etale motivic stable homotopy theory

@article{Bachmann2018RigidityIE,
title={Rigidity in etale motivic stable homotopy theory},
author={Tom Bachmann},
journal={arXiv: K-Theory and Homology},
year={2018}
}
• Tom Bachmann
• Published 2018
• Mathematics
• arXiv: K-Theory and Homology
For a scheme X, denote by SH(X_et^hyp) the stabilization of the hypercompletion of its etale infty-topos, and by SH_et(X) the localization of the stable motivic homotopy category SH(X) at the (desuspensions of) etale hypercovers. For a stable infty-category C, write C_p^comp for the p-completion of C. We prove that under suitable finiteness hypotheses, and assuming that p is invertible on X, the canonical functor e_p^comp: SH(X_et^hyp)_p^comp -> SH_et(X)_p^comp is an equivalence of infty… Expand
6 Citations

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