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 #7457 on tag 0GWI by nhw https://stacks.math.columbia.edu/tag/0GWI#comment-7457 A new comment by nhw on tag 0GWI. In the first line should "categori" be category?

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nhw Sun, 26 Jun 2022 12:25:54 GMT
#7456 on tag 031T by mi https://stacks.math.columbia.edu/tag/031T#comment-7456 A new comment by mi on tag 031T. In the statement of (1), shall we also say a is not a unit?

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mi Sun, 26 Jun 2022 04:36:01 GMT
#7455 on tag 0A38 by WhatJiaranEatsTonight https://stacks.math.columbia.edu/tag/0A38#comment-7455 A new comment by WhatJiaranEatsTonight on tag 0A38. I think here we shall add and but not .

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WhatJiaranEatsTonight Sun, 26 Jun 2022 01:03:50 GMT
#7454 on tag 026B by Hao Peng https://stacks.math.columbia.edu/tag/026B#comment-7454 A new comment by Hao Peng on tag 026B. I am confused by the cocycle condition. My worry is that the composition doesn't make sence: While is a morphism from to , is a morphism from to . Thus it is preassumed that , which is not in general true. Is this a mistake or we insect a natural isomorphism between them, or we can choose the cleavage such that this is true for any fiber products?

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Hao Peng Sat, 25 Jun 2022 03:52:35 GMT
#7453 on tag 0539 by Hao Peng https://stacks.math.columbia.edu/tag/0539#comment-7453 A new comment by Hao Peng on tag 0539. Sorry, in the argument above, change " is a domain" to " is torsion-free".

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Hao Peng Fri, 24 Jun 2022 04:24:47 GMT
#7452 on tag 0539 by Hao Peng https://stacks.math.columbia.edu/tag/0539#comment-7452 A new comment by Hao Peng on tag 0539. I noticed that after minor change this lemma holds for a Bezout domain too:

Let where , then consider , thus for some , and for some . Because is a domain, , so we can take , where . Then .

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Hao Peng Fri, 24 Jun 2022 04:14:36 GMT
#7451 on tag 0AMA by Logan Hyslop https://stacks.math.columbia.edu/tag/0AMA#comment-7451 A new comment by Logan Hyslop on tag 0AMA. I believe there may be a rather minor typo in Lemma 14.19.2, specifically "Taking " should say "Taking ."

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Logan Hyslop Thu, 23 Jun 2022 04:46:34 GMT
#7450 on tag 0E7M by Christophe Marciot https://stacks.math.columbia.edu/tag/0E7M#comment-7450 A new comment by Christophe Marciot on tag 0E7M. In the intro at \emph{we conclude these points are nodes and smooth points on both} and , would it a bit better for comprehension to add a \emph{respectively} after the ?

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Christophe Marciot Thu, 23 Jun 2022 01:25:03 GMT
#7449 on tag 032M by Laurent Moret-Bailly https://stacks.math.columbia.edu/tag/032M#comment-7449 A new comment by Laurent Moret-Bailly on tag 032M. @ #7448: True, but if is a noetherian domain with perfect fraction field of char. , then . Otherwise, by Krull-Akizuki, there is a discrete valuation ring between and , and a uniformizer of cannot be a -th power in . (There may be simpler arguments).

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Laurent Moret-Bailly Thu, 23 Jun 2022 09:30:42 GMT
#7448 on tag 032M by Haohao Liu https://stacks.math.columbia.edu/tag/032M#comment-7448 A new comment by Haohao Liu on tag 032M. From the proof we see that the condition "fraction field has characteristic zero " can be relaxed to "fraction field is perfect".

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Haohao Liu Thu, 23 Jun 2022 03:33:54 GMT