The Stacks project

Comments 1 to 20 out of 6884 in reverse chronological order.

\begin{equation*} \DeclareMathOperator\Coim{Coim} \DeclareMathOperator\Coker{Coker} \DeclareMathOperator\Ext{Ext} \DeclareMathOperator\Hom{Hom} \DeclareMathOperator\Im{Im} \DeclareMathOperator\Ker{Ker} \DeclareMathOperator\Mor{Mor} \DeclareMathOperator\Ob{Ob} \DeclareMathOperator\Sh{Sh} \DeclareMathOperator\SheafExt{\mathcal{E}\mathit{xt}} \DeclareMathOperator\SheafHom{\mathcal{H}\mathit{om}} \DeclareMathOperator\Spec{Spec} \newcommand\colim{\mathop{\mathrm{colim}}\nolimits} \newcommand\lim{\mathop{\mathrm{lim}}\nolimits} \newcommand\Qcoh{\mathit{Qcoh}} \newcommand\Sch{\mathit{Sch}} \newcommand\QCohstack{\mathcal{QC}\!\mathit{oh}} \newcommand\Cohstack{\mathcal{C}\!\mathit{oh}} \newcommand\Spacesstack{\mathcal{S}\!\mathit{paces}} \newcommand\Quotfunctor{\mathrm{Quot}} \newcommand\Hilbfunctor{\mathrm{Hilb}} \newcommand\Curvesstack{\mathcal{C}\!\mathit{urves}} \newcommand\Polarizedstack{\mathcal{P}\!\mathit{olarized}} \newcommand\Complexesstack{\mathcal{C}\!\mathit{omplexes}} \newcommand\Pic{\mathop{\mathrm{Pic}}\nolimits} \newcommand\Picardstack{\mathcal{P}\!\mathit{ic}} \newcommand\Picardfunctor{\mathrm{Pic}} \newcommand\Deformationcategory{\mathcal{D}\!\mathit{ef}} \end{equation*}

On T.C. left comment #7380 on Lemma 10.12.9 in Commutative Algebra

In the second proof, shouldn't it be instead of ?


On Matthieu Romagny left comment #7379 on Lemma 15.11.8 in More on Algebra

Yes, it is in the SP, see for instance Lemma 01WM.


On Laurent Moret-Bailly left comment #7378 on Lemma 15.11.8 in More on Algebra

@#7377: A universal homeomorphism is integral (EGA IV, 18.12.10). So perhaps this should be (resp. already is) in the Stacks Project.


On comment_bot left comment #7377 on Lemma 15.11.8 in More on Algebra

It may be useful to include the statement that the same holds for any that is a universal homeomorphism on spectra (sorry if this is already in the Stacks Project but I missed it!). I think this follows from the characterization of Henselian pairs in terms of lifting idempotents.


On Sriram left comment #7376 on Lemma 15.91.3 in More on Algebra

Hello!

In the proof of (2), showing the surjection of the canonical map to completion, the sequence of equations must have an "f" in the coefficient of x_1. That is, " ... = x-x_0+f e_1 = x-x_0 -f x_1 + f^2 e_2 = ..."

Thanks


On Torsten Wedhorn left comment #7375 on Lemma 37.21.7 in More on Morphisms

A rather trivial observation: The flatness hypothesis on seems to be superfluous except for (1) because of openness of flatness. So I think, one could slightly strengthen the result by supposing only that is locally of finite presentation and add in (1) the condition that is flat in in the description of .

Sorry, I just realized that the flatness is of course also needed for (3). So please forget my comment.


On Yiming TANG left comment #7374 on Section 10.134 in Commutative Algebra

In tag 00S1, "φ:P→P is a morphism of presentations from α to α′" should be "φ:P→P' is a morphism of presentations from α to α′".


On DatPham left comment #7373 on Lemma 86.19.7 in Formal Algebraic Spaces

I think it would be better to indicate where we use the assumption that is representable by algebraic spaces. I guess this is used to ensure that is a quasi-compact algebraic space, hence admits an \' etale cover by an affine scheme ; the composite then factors through some , and the same is true for by the sheaf property.


On Torsten Wedhorn left comment #7372 on Lemma 37.21.7 in More on Morphisms

A rather trivial observation: The flatness hypothesis on seems to be superfluous except for (1) because of openness of flatness. So I think, one could slightly strengthen the result by supposing only that is locally of finite presentation and add in (1) the condition that is flat in in the description of .


On 代数几何真难 left comment #7371 on Section 31.24 in Divisors

OK. I see. Even though can not be lifted to an element in in general, it can be lifted to an element in , which makes well-defined.


On XYETALE left comment #7370 on Section 10.113 in Commutative Algebra

I checked a bit that the notation probably has never defined for a ring, only for fields. Maybe it is a bit clearer to mention what it means.


On 代数几何真难 left comment #7369 on Section 31.24 in Divisors

I think in lemma 31.24.2, in order to define as a section in , one should first lift to a global section . But is not surjective, seems that is not well-defined.


On Alekos Robotis left comment #7368 on Section 37.11 in More on Morphisms

In definition 37.1.11, there is a slight typo : it says "soure" instead of "source."


On Shizhang left comment #7367 on Lemma 13.27.7 in Derived Categories

Maybe the vertical arrows should all go downward?


On David Holmes left comment #7366 on Section 10.34 in Commutative Algebra

Hi Zongzhu Lin, I think 005K might be the reference you are looking for? Alternatively, I think it's not so hard to see the claim from the definition of constructibility.


On left comment #7365 on Section 111.3 in A Guide to the Literature

The page has been archived by the Wayback Machine. At least some parts of the book are still available through it: https://web.archive.org/web/20110707004531/http://www.math.uzh.ch/index.php?pr_vo_det&key1=1287&key2=580&no_cache=1


On Yijin Wang left comment #7364 on Lemma 28.22.11 in Properties of Schemes

Typo in the proof of lemma 28.22.11: the first sentence should be 'A_1,A_2 ⊂A'


On Alex Ivanov left comment #7363 on Lemma 29.35.16 in Morphisms of Schemes

In (2), it should in fact suffice to assume that is locally of finite type over . (This is also consistent with Lemma 02FW, to which the proof refers).


On left comment #7362 on Section 10.34 in Commutative Algebra

@7361: That is a limitation of how things are being displayed. There is a work-around possible, the question is whether there are enough cases of this causing confusion to put in the effort. I'll put it on the possible features list though, thanks for noticing!


On Laurent Moret-Bailly left comment #7361 on Section 10.34 in Commutative Algebra

Strangely, in "tags" mode, parts (1) and (2) are also converted to tags in the proof (but not in the statement).