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On pp 46 of his Eisenstein Ideal paper, Mazur states Theorem I.4 and in the discussion that follows, he mentions 'a standard patching argument' that completes the proof. I was wondering whether this is the same as the gluing lemma that's described in Hartshorne, or is Mazur referring to something else? I'd appreciate if someone can fill me in on the details or perhaps direct me to some reference.

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In general this is fpqc descent, for a cover you should write down. In this particular case one can also appeal to a simpler criterion, such as the one given by B. Bhatt here: –  user1594 Jun 15 '11 at 15:53
Thanks for the link. –  Saikat Biswas Jun 17 '11 at 15:21

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