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 #5013 on tag 09XI by Laurent Moret-Bailly https://stacks.math.columbia.edu/tag/09XI#comment-5013 A new comment by Laurent Moret-Bailly on tag 09XI. In the references, the link to "Gabber-henselian" doesn't work.

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Laurent Moret-Bailly Sat, 04 Apr 2020 09:56:10 GMT
#5012 on tag 0C1B by Elyes Boughattas https://stacks.math.columbia.edu/tag/0C1B#comment-5012 A new comment by Elyes Boughattas on tag 0C1B. Typo in the Riemann-Hurwitz formula preceding lemma 0C1C: should be .

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Elyes Boughattas Sat, 04 Apr 2020 09:30:35 GMT
#5011 on tag 0DYD by Laurent Moret-Bailly https://stacks.math.columbia.edu/tag/0DYD#comment-5011 A new comment by Laurent Moret-Bailly on tag 0DYD. Suggested corollary: If and are henselian pairs, so is .

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Laurent Moret-Bailly Sat, 04 Apr 2020 09:11:07 GMT
#5010 on tag 04VB by JoseTomas https://stacks.math.columbia.edu/tag/04VB#comment-5010 A new comment by JoseTomas on tag 04VB. I think Lemma 4.26.6 can be simplified (even improved): where equalities are in the category and we are left composing with in this category (use of functor is implied).

And in if, and only if, exists such that where the equality is now in . So I think, in reality, condition does not depends on

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JoseTomas Tue, 31 Mar 2020 07:36:13 GMT
#5009 on tag 0B8B by Matthieu Romagny https://stacks.math.columbia.edu/tag/0B8B#comment-5009 A new comment by Matthieu Romagny on tag 0B8B. And is duplicated.

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Matthieu Romagny Tue, 31 Mar 2020 01:42:32 GMT
#5008 on tag 0B8B by Laurent Moret-Bailly https://stacks.math.columbia.edu/tag/0B8B#comment-5008 A new comment by Laurent Moret-Bailly on tag 0B8B. Typo in statement: "for every " should be "for every ".

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Laurent Moret-Bailly Tue, 31 Mar 2020 09:26:31 GMT
#5007 on tag 032L by Laurent Moret-Bailly https://stacks.math.columbia.edu/tag/032L#comment-5007 A new comment by Laurent Moret-Bailly on tag 032L. If is not noetherian, the integral closure is still contained in a finite -submodule of . This can be useful, and moreover it is the key point in the proof, so it could be worth stating.

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Laurent Moret-Bailly Mon, 30 Mar 2020 12:05:26 GMT
#5006 on tag 0333 by Rankeya https://stacks.math.columbia.edu/tag/0333#comment-5006 A new comment by Rankeya on tag 0333. It seems to me that the above characterization is an if and only if. Namely, if is N-1 and is its normalization, then since is generically an isomorphism, there must exist some such that is an isomorphism. Thus if is N-1 then (1) holds, while (2) follows because N-1 behaves well under localization by an earlier lemma.

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Rankeya Mon, 30 Mar 2020 11:39:55 GMT
#5005 on tag 01NL by Laurent Moret-Bailly https://stacks.math.columbia.edu/tag/01NL#comment-5005 A new comment by Laurent Moret-Bailly on tag 01NL. The image of should be , not .

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Laurent Moret-Bailly Sun, 29 Mar 2020 09:26:56 GMT
#5004 on tag 01MG by Laurent Moret-Bailly https://stacks.math.columbia.edu/tag/01MG#comment-5004 A new comment by Laurent Moret-Bailly on tag 01MG. I guess the degree of each should be .

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Laurent Moret-Bailly Sun, 29 Mar 2020 09:08:52 GMT