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: $g_x$ should be $g_X$.

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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 $(A,I)$ and $(A,I')$ are henselian pairs, so is $(A,I+I')$.

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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): $A=B \iff s^{-1}f=s^{-1}g \iff f=g$ where equalities are in the category $S^{-1}C$ and we are left composing with $s$ in this category (use of functor $Q$ is implied).

And $f=g$ in $S^{-1}C$ if, and only if, exists $t \in S$ such that $tf=tg$ where the equality is now in $C$. So I think, in reality, condition does not depends on $s$

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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 $f:X\to Y$ 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 $T\to X$" should be "for every $T\to Y$".

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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 $R$ is not noetherian, the integral closure is still contained in a finite $R$-submodule of $L$. 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 $R$ is N-1 and $R^N$ is its normalization, then since $R \rightarrow R^N$ is generically an isomorphism, there must exist some $f \in R$ such that $R_f \rightarrow R^N_f$ is an isomorphism. Thus if $R$ 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 $C$ should be $X_2^2$, not $X_2^3$.

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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 $X_i$ should be $1$.

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