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 #4535 on tag 09GZ by Ashutosh https://stacks.math.columbia.edu/tag/09GZ#comment-4535 A new comment by Ashutosh on tag 09GZ. Second paragraph of Lemma 09H9 may be needs a line saying that now we prove that $K/F$ is separable.

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Ashutosh Sat, 14 Sep 2019 07:09:27 GMT
#4531 on tag 00JP by BB https://stacks.math.columbia.edu/tag/00JP#comment-4531 A new comment by BB on tag 00JP. I think there's a small typo in the last paragraph of the proof, in the third to last sentence: I think you want to say IS_f \neq S_f to conclude that (S/I)_f is not zero.

Also, perhaps I missed something, but I could not find anywhere in the proof refereeing to parts (8) or (9) of the lemma.

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BB Thu, 12 Sep 2019 09:37:17 GMT
#4530 on tag 0CDM by 李时璋 https://stacks.math.columbia.edu/tag/0CDM#comment-4530 A new comment by 李时璋 on tag 0CDM. very very small issue, on the first line you had 768g, but on the second line you were saying 728g.

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#4529 on tag 00AR by Aniruddh Agarwal https://stacks.math.columbia.edu/tag/00AR#comment-4529 A new comment by Aniruddh Agarwal on tag 00AR. Trivial remark: in (45), should the article "a" be used instead of "an"?

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Aniruddh Agarwal Tue, 10 Sep 2019 12:49:58 GMT
#4528 on tag 0106 by Johan https://stacks.math.columbia.edu/tag/0106#comment-4528 A new comment by Johan on tag 0106. Usually, in a situation like this when we are definining a blah which is unique up to isomorphism in the definiition we say "a blah" and then in a comment after the definition we say that because the thing is unique up to unique isomorphism we will from now on use the terminology "the blah". See the text following this definition in Section 12.3.

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Johan Mon, 09 Sep 2019 08:30:53 GMT
#4527 on tag 086Q by awllower https://stacks.math.columbia.edu/tag/086Q#comment-4527 A new comment by awllower on tag 086Q. Two minor typos:

should be

And should be

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awllower Sun, 08 Sep 2019 10:07:41 GMT
#4526 on tag 01DZ by Théo de Oliveira Santos https://stacks.math.columbia.edu/tag/01DZ#comment-4526 A new comment by Théo de Oliveira Santos on tag 01DZ. A few trivial typos: Let F be a abelian sheaf Extra parenthesis: The family of functors $H_i((X,−)$ forms [...] from $Ab(X)\rightarrow Ab$ Extra parenthesis*: The family of functors $H_i((X,−)$ forms [...] from $Mod(\mathcal{O}_X)\rightarrow Mod_{\mathcal{O}_X(X)}$

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Théo de Oliveira Santos Sun, 08 Sep 2019 06:47:11 GMT
#4525 on tag 0106 by Aniruddh Agarwal https://stacks.math.columbia.edu/tag/0106#comment-4525 A new comment by Aniruddh Agarwal on tag 0106. This is a very minor point, but is there a reason for using the terminology "a cokernel", etc. instead of "the cokernel", etc. when these objects are unique upto unique iso? ]]> Aniruddh Agarwal Sun, 08 Sep 2019 03:37:25 GMT #4524 on tag 00MH by Johan https://stacks.math.columbia.edu/tag/00MH#comment-4524 A new comment by Johan on tag 00MH. Yes very good. The key is that here $u$ is surjective whereas in Lemma 10.98.1 it doesn't need to be.

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Johan Fri, 06 Sep 2019 06:40:03 GMT
#4523 on tag 00MH by Ronnie https://stacks.math.columbia.edu/tag/00MH#comment-4523 A new comment by Ronnie on tag 00MH. To show $u$ is injective, may be we can also argue as follows. Let $K$ denote the kernel of $u$, it is a finite $S$ module. Since $M$ is flat over $R$, applying $-\otimes_RR/\mathfrak{m}$ we get $K\otimes_RR/\mathfrak{m}=0$. It follows that $K\otimes_SS/\mathfrak{m}S=0$, which shows, by Nakayama's lemma, that $K=0$.

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Ronnie Fri, 06 Sep 2019 04:57:51 GMT