The Stacks project

Remark 15.90.21. In [Beauville-Laszlo] it is assumed that $f$ is a nonzerodivisor in $R$ and $R' = R^\wedge $, which gives a glueing pair by Lemma 15.90.7. Even in this setting Theorem 15.90.17 says something new: the results of [Beauville-Laszlo] only apply to modules on which $f$ is a nonzerodivisor (and hence glueable in our sense, see Lemma 15.90.11). Lemma 15.90.20 also provides a slight extension of the results of [Beauville-Laszlo]: not only can we allow $M$ to have nonzero $f$-power torsion, we do not even require it to be glueable.

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