Fibrant presheaves of spectra and Guillen-Navarro extension

Abstract

In this remark we prove that the Guill´en-Navarro extension of a presheaf of spectra in the category of algebraic varieties over a field of characteristic zero, when exists, coincides up to weak equivalence with the fibrant replacement of the presheaf in the injective model category structure with the cd-topology of abstract blow-ups.