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 #9308 on tag 08XA by Stacks project https://stacks.math.columbia.edu/tag/08XA#comment-9308 A new comment by Stacks project on tag 08XA. OK, the typo is that a subscript was missing on the in the sentence, right? I fixed that. But I think it immediately follows from that sentence that is is an isomorphism. I did add another reference to the first sentence of the last paragraph to clarify. Changes here.

]]>
Stacks project Fri, 24 May 2024 02:46:47 GMT
#9307 on tag 09ZF by Fiasco https://stacks.math.columbia.edu/tag/09ZF#comment-9307 A new comment by Fiasco on tag 09ZF. In the end of proof of lemma, why does Zariski locally come from a section of ? And why are these local sections compatible such that they can glue altogether?

For the first question, let's be more careful(with the same notations). Let be an open subscheme which factors through for some . So defines a section of named , we want to show its restriction is equal to . Note that has an etale cover , So we only need to check each piece . We look at the stalks and choose a geometric point .

On the one hand, the stalk of restriction of is just the stalk of at pt, which is considered as a geometric point of .

On the other hand, the stalk of is just the stalk of at pt, which is considered as a geometric point of .

Now the key point is we only know pt factors through . But by definition and coincide at some scheme which is etale over such that and both factor through . So can be strictly "smaller" than .

]]>
Fiasco Fri, 24 May 2024 12:49:29 GMT
#9306 on tag 0BXJ by Stacks project https://stacks.math.columbia.edu/tag/0BXJ#comment-9306 A new comment by Stacks project on tag 0BXJ. Good catch! OK, I rewrote the proof to make it work in the non-Noetherian case. More interesting was the case of Lemma 31.28.4. Finally, Lemma 31.31.3 was unfixable and I needed to assume the Noetherian assumption. See these changes.

]]>
Stacks project Wed, 22 May 2024 03:56:56 GMT
#9305 on tag 090B by Stacks project https://stacks.math.columbia.edu/tag/090B#comment-9305 A new comment by Stacks project on tag 090B. Thanks and fixed here.

]]>
Stacks project Wed, 22 May 2024 02:31:56 GMT
#9304 on tag 004D by Stacks project https://stacks.math.columbia.edu/tag/004D#comment-9304 A new comment by Stacks project on tag 004D. Fixed.

]]>
Stacks project Wed, 22 May 2024 02:22:04 GMT
#9303 on tag 0H6X by Stacks project https://stacks.math.columbia.edu/tag/0H6X#comment-9303 A new comment by Stacks project on tag 0H6X. Dear Cop 223, I understand what you are saying, but in the setup as in this chapter, I do not think this "helps".

]]>
Stacks project Wed, 22 May 2024 02:20:40 GMT
#9302 on tag 0B40 by Stacks project https://stacks.math.columbia.edu/tag/0B40#comment-9302 A new comment by Stacks project on tag 0B40. Yes. Going to leave as is.

]]>
Stacks project Wed, 22 May 2024 02:08:48 GMT
#9301 on tag 0A9W by Stacks project https://stacks.math.columbia.edu/tag/0A9W#comment-9301 A new comment by Stacks project on tag 0A9W. Indeed. Weakend assumptions here.

]]>
Stacks project Wed, 22 May 2024 02:03:42 GMT
#9300 on tag 0F4V by Stacks project https://stacks.math.columbia.edu/tag/0F4V#comment-9300 A new comment by Stacks project on tag 0F4V. this.

]]>
Stacks project Wed, 22 May 2024 01:59:29 GMT
#9299 on tag 0B1J by Stacks project https://stacks.math.columbia.edu/tag/0B1J#comment-9299 A new comment by Stacks project on tag 0B1J. Good catch! Fixed here.

]]>
Stacks project Wed, 22 May 2024 01:55:39 GMT