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 #8475 on tag 08JZ by Et https://stacks.math.columbia.edu/tag/08JZ#comment-8475 A new comment by Et on tag 08JZ. Is the map a splitting? If so it would be clearer to just deduce injectivity from that.

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Et Fri, 09 Jun 2023 07:20:19 GMT
#8474 on tag 00S2 by Et https://stacks.math.columbia.edu/tag/00S2#comment-8474 A new comment by Et on tag 00S2. Suggestion: since this proposition uses multiple rings, maybe add a subscript for the tensor products indicating over what they are taken

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Et Fri, 09 Jun 2023 07:06:06 GMT
#8473 on tag 0AS8 by Et https://stacks.math.columbia.edu/tag/0AS8#comment-8473 A new comment by Et on tag 0AS8. Where is the induction here specifically done? Wouldn't it be enough just to replace R by R/I^k+1, M by M/I^k+1 and I by I/I^k+1 and apply the precceding lemma?

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Et Thu, 08 Jun 2023 09:02:28 GMT
#8472 on tag 051C by Et https://stacks.math.columbia.edu/tag/051C#comment-8472 A new comment by Et on tag 051C. Maybe note in the almost last paragraph that you are using the snake lemma? Took me a moment to figure out what you were trying to do

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Et Thu, 08 Jun 2023 08:24:42 GMT
#8471 on tag 009F by Paul https://stacks.math.columbia.edu/tag/009F#comment-8471 A new comment by Paul on tag 009F. I guess in the proof of (2) and (4) the notation was heavily relaxed, since why should hold, actually it holds for some restriction of s and s'. Also it should be or better of some . I recommend to mention it or rework completly the proof.

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Paul Thu, 08 Jun 2023 05:03:19 GMT
#8470 on tag 00KZ by Laurent Moret-Bailly https://stacks.math.columbia.edu/tag/00KZ#comment-8470 A new comment by Laurent Moret-Bailly on tag 00KZ. In the proof, the minimality of is not needed, so "a finite set of generators" would be more to the point. Also, it would be worth pointing out that the 's are finite modules, and perhaps that the last quotient is finitely presented if is.

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Laurent Moret-Bailly Thu, 08 Jun 2023 01:57:56 GMT
#8469 on tag 03L7 by Ryo Suzuki https://stacks.math.columbia.edu/tag/03L7#comment-8469 A new comment by Ryo Suzuki on tag 03L7. I think Lemma 03GI is used to deduce is quasi-compact. It might worth to note it explicitly.

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Ryo Suzuki Wed, 07 Jun 2023 11:05:29 GMT
#8468 on tag 01KR by Elías Guisado https://stacks.math.columbia.edu/tag/01KR#comment-8468 A new comment by Elías Guisado on tag 01KR. For the sake of having some reference that is actually instructive, here's a neat proof of the cartesianity of the square https://mathoverflow.net/a/80812/101848

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Elías Guisado Wed, 07 Jun 2023 09:59:47 GMT
#8467 on tag 01KP by Elías Guisado https://stacks.math.columbia.edu/tag/01KP#comment-8467 A new comment by Elías Guisado on tag 01KP. Minor typo: instead of in "we see that can be identified with ," one should write .

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Elías Guisado Wed, 07 Jun 2023 07:54:26 GMT
#8466 on tag 01JY by Elías Guisado https://stacks.math.columbia.edu/tag/01JY#comment-8466 A new comment by Elías Guisado on tag 01JY. I think it could be nice to reference https://stacks.math.columbia.edu/tag/001U#comment-3413 to make explicit the formal nature of the argument (I believe such little hints are quite useful for those recently initiated to algebraic geometry—and often to category theory too—reading this webpage, like the version of myself one year ago).

An alternative reformulation of the proof would be by placing this lemma after remark https://stacks.math.columbia.edu/tag/01JW#comment-8464 and then just invoking the remark plus 26.17.6.

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Elías Guisado Wed, 07 Jun 2023 07:13:33 GMT