Stacks project -- Comments https://stacks.math.columbia.edu/recent-comments.xml Stacks project, see https://stacks.math.columbia.edu en stacks.project@gmail.com (The Stacks project) pieterbelmans@gmail.com (Pieter Belmans) https://stacks.math.columbia.edu/static/stacks.png Stacks project -- Comments https://stacks.math.columbia.edu/recent-comments.rss #8745 on tag 010G by Anonymous https://stacks.math.columbia.edu/tag/010G#comment-8745 A new comment by Anonymous on tag 010G. If " is left inverse to " means that is the identity (where means "apply first"), then I think "left" and "right" should be switched in this lemma.

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Anonymous Sat, 09 Dec 2023 01:51:50 GMT
#8744 on tag 05N4 by Matt Broe https://stacks.math.columbia.edu/tag/05N4#comment-8744 A new comment by Matt Broe on tag 05N4. Someone pointed out to me that this claim holds in more generality: finitely generated projective modules are dualizable objects in RMod, and tensoring with dualizable objects commutes with limits.

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Matt Broe Fri, 08 Dec 2023 01:11:36 GMT
#8743 on tag 01XT by Zhenhua Wu https://stacks.math.columbia.edu/tag/01XT#comment-8743 A new comment by Zhenhua Wu on tag 01XT. I believe the lemma is wrong in the case . Unwrapping the definition we should have , which is compatitable with but not compatitable with when .

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Zhenhua Wu Thu, 07 Dec 2023 04:42:06 GMT
#8742 on tag 05N4 by Matt Broe https://stacks.math.columbia.edu/tag/05N4#comment-8742 A new comment by Matt Broe on tag 05N4. I have found the criterion given in claim 1 of the following link for commuting tensor with an inverse limit of modules useful, but have not seen it in any reference: https://math.stackexchange.com/a/4577954/304290 Perhaps it would be worth mentioning here, either on this tag or wherever else it would fit.

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Matt Broe Tue, 05 Dec 2023 05:46:03 GMT
#8741 on tag 0GZ3 by Zongzhu Lin https://stacks.math.columbia.edu/tag/0GZ3#comment-8741 A new comment by Zongzhu Lin on tag 0GZ3. In the definition of Koszul complex , should the differential be defined by ?

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Zongzhu Lin Mon, 04 Dec 2023 09:27:42 GMT
#8740 on tag 0323 by pkas https://stacks.math.columbia.edu/tag/0323#comment-8740 A new comment by pkas on tag 0323. In the second part of the proof for 10.160.8 (the case of positive characteristic), the terminology is slightly confusing. I suggest rewording the condition required of to the commutative square , where are the projections and , and is a chosen isomorphism. Moreover, the map to lift using formal smoothness is the composition .

It could also be helpful for readers to mention that this proof shows that the map from Cohen rings (up to isomorphism) to fields (up to isomorphism) is injective.

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pkas Sat, 02 Dec 2023 04:37:27 GMT
#8739 on tag 05JF by Paolo Lammens https://stacks.math.columbia.edu/tag/05JF#comment-8739 A new comment by Paolo Lammens on tag 05JF. Here what is the ideal that defines the -adic topology/completion?

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Paolo Lammens Fri, 01 Dec 2023 07:38:31 GMT
#8738 on tag 0EY5 by Yicheng Zhou https://stacks.math.columbia.edu/tag/0EY5#comment-8738 A new comment by Yicheng Zhou on tag 0EY5. I guess that in the first sentence of the last paragraph should be only "geometrically connected"?

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Yicheng Zhou Wed, 29 Nov 2023 10:42:23 GMT
#8737 on tag 03K8 by Mudassar Hameed https://stacks.math.columbia.edu/tag/03K8#comment-8737 A new comment by Mudassar Hameed on tag 03K8. Thanks for sharing this useful information.

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Mudassar Hameed Wed, 29 Nov 2023 06:58:07 GMT
#8736 on tag 00H9 by Alexis https://stacks.math.columbia.edu/tag/00H9#comment-8736 A new comment by Alexis on tag 00H9. For lemma 0BBY, you might also want that .

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Alexis Wed, 29 Nov 2023 03:46:14 GMT