Stacks project -- Comments
http://stacks.math.columbia.edu/comments-feed.rss
Stacks project, see http://stacks.math.columbia.eduenstacks.project@gmail.com (Stacks Project)pieterbelmans@gmail.com (Pieter Belmans)http://stacks.math.columbia.edu/stacks.pngStacks project -- Comments
http://stacks.math.columbia.edu/comments-feed.rss
#2769 on tag 0687 by Sándor Kovács
http://stacks.math.columbia.edu/tag/0687#comment-2769
A new comment by Sándor Kovács on tag 0687.Shouldn't this be Lemma 36.50.1?
]]>Sándor Kovács Tue, 15 Aug 2017 17:09:57 +0000#2768 on tag 01KP by sdf
http://stacks.math.columbia.edu/tag/01KP#comment-2768
A new comment by sdf on tag 01KP.Yes I didn't read it properly, apologies.
]]>sdfFri, 11 Aug 2017 17:06:04 +0000#2767 on tag 02JQ by sdf
http://stacks.math.columbia.edu/tag/02JQ#comment-2767
A new comment by sdf on tag 02JQ.There is a fairly standard notation of $\mathrm{ff}$ or $\mathrm{FF}$ or $\mathrm{FoF}$ for field of fractions at least in my part of the world. But having a full-stop as part of the notation is aesthetically less than ideal, this has been pointed out before I think.
]]>sdfFri, 11 Aug 2017 17:03:34 +0000#2766 on tag 02JQ by BCnrd
http://stacks.math.columbia.edu/tag/02JQ#comment-2766
A new comment by BCnrd on tag 02JQ.Dario's suggestion of $\kappa(\mathfrak{p})$ for the fraction field of $A/\mathfrak{p}$ seems fine since such notation has been standard from EGA, and I think the meaning of ${\rm{Frac}}$ is also immediately recognized by anyone, but I am not a fan of $Q(\cdot)$ to denote the fraction field of a domain since it is not sufficiently universally known and so potentially a bit obscure (though admittedly anyone who has actually understood the proof up to there can infer what it must mean). In a work this massive, which essentially nobody reads linearly, it is best not to use slightly non-standard notation unless there is an easily-identified and systematically maintained list of all such notation, but alas there seems to be no such list; the Notation section in the "Preliminaries" Part is a bit brief!)
]]>BCnrdFri, 11 Aug 2017 00:18:11 +0000#2765 on tag 02JQ by Dario Weißmann
http://stacks.math.columbia.edu/tag/02JQ#comment-2765
A new comment by Dario Weißmann on tag 02JQ.Why not use the notation $Q(-)$ introduced in Example 10.9.8 (3)?
Or - as in this case we are talking about the residue field at a prime - use the notation $\kappa(-)$ introduced in 25.2.1 (2)?
]]>Dario WeißmannThu, 10 Aug 2017 20:58:25 +0000#2764 on tag 08XU by Dario Weißmann
http://stacks.math.columbia.edu/tag/08XU#comment-2764
A new comment by Dario Weißmann on tag 08XU.This result is also stated in Lemma 19.2.6, is this intentional?
In Lemma 19.2.6 (or rather directely above) this is called "criterion of Baer". I think it's quite nice that the result has a name, although "Baer's criterion" sounds better.
]]>Dario WeißmannThu, 10 Aug 2017 20:35:31 +0000#2763 on tag 0APG by BCnrd
http://stacks.math.columbia.edu/tag/0APG#comment-2763
A new comment by BCnrd on tag 0APG.To prove the instance of (34.15.0.1) that is relevant in this proof, namely ${U_i}$ an inverse system (under reverse inclusions) of quasi-compact open subspaces of a spectral space (rather than some more abstract kind of inverse system), one does not need the extreme generality of the links given above to prove it. Namely, one can given a less notationally intensive argument using basic "spreading out" properties involving quasi-compact open subsets, pro-constructible subsets, and open covers thereof in spectral spaces. I mention this because when trying to follow the links given for the proof of (34.15.0.1), one encounters a blizzard of notation which is unpleasant to unravel and too heavy for the actual situation relevant here. I found it easier to make my own proof of the relevant special case than to try to decipher whatever is going on in the given links. How about giving a Lemma here (or Corollary elsewhere) that focuses on the relevant special case of (34.15.0.1) with quasi-compact open subsets in a spectral space and gives a direct proof in that case, saving the ready from wading through the extra generality and heavier notation in the links presently given?
]]>BCnrdThu, 10 Aug 2017 18:17:52 +0000#2762 on tag 02JQ by BCnrd
http://stacks.math.columbia.edu/tag/02JQ#comment-2762
A new comment by BCnrd on tag 02JQ.The notation $f.f.$ to denote "fraction field" (twice) near the end of the proof seems kind of awful (not only because in the argument there is a map called $f$). Is this really the standard notation in this document? Why not ${\rm{Frac}}$ instead?
]]>BCnrdThu, 10 Aug 2017 16:35:37 +0000#2761 on tag 03AG by Anonymous
http://stacks.math.columbia.edu/tag/03AG#comment-2761
A new comment by Anonymous on tag 03AG.Typos? On this page both $\mathcal{G}$ and $G$ are repeatedly used for what (I think) should be the same object.
]]>AnonymousSun, 06 Aug 2017 07:26:19 +0000#2760 on tag 07FE by Anonymous
http://stacks.math.columbia.edu/tag/07FE#comment-2760
A new comment by Anonymous on tag 07FE.Towards the end of the proof it should say $R_\mathfrak{p} \rightarrow \Lambda_\mathfrak{q}$ is flat by Algebra, Lemma 10.127.2.
And the following map should map from $R_\mathfrak{p}/(x_1^e,\dots,x_d^e)$.
]]>AnonymousSat, 05 Aug 2017 14:46:31 +0000