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 #3518 on tag 021Z by Raymond Cheng https://stacks.math.columbia.edu/tag/021Z#comment-3518 A new comment by Raymond Cheng on tag 021Z. Heh. This goes all the way through the other topologies too. This is what happens when you copy and paste, starting with "├ętale"...

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Raymond Cheng Thu, 16 Aug 2018 07:11:13 GMT
#3517 on tag 021Z by Samir Canning https://stacks.math.columbia.edu/tag/021Z#comment-3517 A new comment by Samir Canning on tag 021Z. small typo: "an smooth" should be "a smooth."

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Samir Canning Thu, 16 Aug 2018 12:18:44 GMT
#3510 on tag 095S by Daniel Levine https://stacks.math.columbia.edu/tag/095S#comment-3510 A new comment by Daniel Levine on tag 095S. Typo: I believe the the second in the morphism in Theorem 095T should be .

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Daniel Levine Mon, 13 Aug 2018 10:13:55 GMT
#3509 on tag 02MB by Dmitrii https://stacks.math.columbia.edu/tag/02MB#comment-3509 A new comment by Dmitrii on tag 02MB. In the proof of Lemma 02MJ it says "In this case the left hand side of the formula"; I think this should be replaced by the "right hand side of the formula".

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Dmitrii Fri, 10 Aug 2018 03:37:04 GMT
#3508 on tag 01PV by Yicheng Zhou https://stacks.math.columbia.edu/tag/01PV#comment-3508 A new comment by Yicheng Zhou on tag 01PV. By using direction (2) to (1) of Lemma 28.11.3, one can give a more schematic proof as follows. By hypothesis we have locally , therefore the open immersion is locally given by a principal open set (in an affine neighborhood). By the lemma cited, is affine, therfore is affine whenever is affine.

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Yicheng Zhou Thu, 09 Aug 2018 09:40:37 GMT
#3507 on tag 00HL by Jonas Ehrhard https://stacks.math.columbia.edu/tag/00HL#comment-3507 A new comment by Jonas Ehrhard on tag 00HL. By the claimed exactness of the diagram we have , and

Then the snake connects .

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Jonas Ehrhard Wed, 08 Aug 2018 04:07:49 GMT
#3506 on tag 00HL by Manuel Hoff https://stacks.math.columbia.edu/tag/00HL#comment-3506 A new comment by Manuel Hoff on tag 00HL. Hi, I think it's better to say "diagram chasing" here than "snake lemma". Seriously though, can somebody explain where the snake is?

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Manuel Hoff Wed, 08 Aug 2018 12:06:52 GMT
#3505 on tag 00K8 by Jonas Ehrhard https://stacks.math.columbia.edu/tag/00K8#comment-3505 A new comment by Jonas Ehrhard on tag 00K8. Lemma 00JD (10.54.1) needs to be Artinian. I don't see why this should be the case, as the ideals

seem to give a possibly infinite descending sequence. . This sequence stabilises iff for , which must not be true. For example consider the localisation of the polynomial ring at the maximal ideal and .

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Jonas Ehrhard Wed, 08 Aug 2018 11:46:24 GMT
#3504 on tag 0BCE by Johan https://stacks.math.columbia.edu/tag/0BCE#comment-3504 A new comment by Johan on tag 0BCE. Dear Ravi, fair question. It is the 5th condition in Lemma 15.70.2. I have edited the proof to clarify. See here.

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Johan Sun, 05 Aug 2018 01:45:28 GMT
#3503 on tag 0BZJ by Johan https://stacks.math.columbia.edu/tag/0BZJ#comment-3503 A new comment by Johan on tag 0BZJ. OK, yes thanks. Fixed here.

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Johan Sun, 05 Aug 2018 01:32:22 GMT