Descent for blow-up's on smooth schemes
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These are the notes of a talk in which we translate from the A1-homotopy theoretic context an argument from [Mor99] showing that a homotopy invariant presheaf of spectra on the category of smooth schemes that satisfies Nisnevich descent automatically satisfies descent for abstract blow-ups. More concretely, Theorem 3.3.1 in [Mor99] roughly says that a Nisnevich distinguished square of schemes is homotopy cartesian when seen in the stable A1-homotopy category. We complete the details of the proof of this theorem and write it in the language of presheaves of spectra. This is theorem 3.7 in this notes.