The Stacks project

Remark 61.6.9. In each of Lemmas 61.6.1, 61.6.2, Proposition 61.6.6, and Lemma 61.6.8 we find an ind-Zariski ring map with some properties. In the paper [BS] the authors use the notion of an ind-(Zariski localization) which is a filtered colimit of finite products of principal localizations. It is possible to replace ind-Zariski by ind-(Zariski localization) in each of the results listed above. However, we do not need this and the notion of an ind-Zariski homomorphism of rings as defined here has slightly better formal properties. Moreover, the notion of an ind-Zariski ring map is the natural analogue of the notion of an ind-├ętale ring map defined in the next section.

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