Real etale motivic homotopy theory over a scheme S is equivalent to sheaves of spaces on the real spectrum of S, and on pointed connected motivic spaces the real etale localization is the rho-telescope.
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Unstable motivic and real-\'etale homotopy theory
Real etale motivic homotopy theory over a scheme S is equivalent to sheaves of spaces on the real spectrum of S, and on pointed connected motivic spaces the real etale localization is the rho-telescope.