“…Proceeding as in the proof of Proposition 4.2, we let P = Spec( P ∈P R P ), let U = Spec( U ∈U R U ), and let B = Spec( ℘∈B R ℘ ). Then patching holds for coherent sheaves on X with respect to P, U , B by [Pri00, Theorem 3.4] (see also [HKL20,Theorem 3.1.4]), as a consequence of [FR70, Proposition 4.2] or [Art70, Theorem 2.6] together with Grothendieck's Existence Theorem ([Gro61, Théorème 5.1.6]). By [HKL20, Corollary 3.0.2], it follows from this patching property that we have the exact sequence asserted in the proposition.…”