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We consider a class of non-reduced valuation rings, known in the literatureas chain rings. We observe that the Grothendieck topology generated by theZariski topology and smooth blowup squares is exactly the topology which haschain rings for its local rings, and that sheaves for this topology are\emph{not} characterised by excision for smooth blowup squares.

Non-reduced valuation rings and descent for smooth blowup squares