The Stacks project

Comments 1 to 20 out of 9309 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 Victor de Vries left comment #10194 on Lemma 63.11.1 in More Étale Cohomology

I have a question about whether an alternative form of this lemma exists: The functor admit a right adjoint for a possibly non-torsion coefficient ring . So for example for , so that we have . I tried checking the references and I do not see any point at which this fails, so I thought I might ask.


On left comment #10193 on Lemma 10.161.8 in Commutative Algebra

What does Lemma 032L state about the integral closure of a Noetherian normal domain? Regard IT Telkom


On Heer left comment #10192 on Lemma 18.33.11 in Modules on Sites

In the last line of the statement, there is a typo "mapsto".


On Shubhankar left comment #10191 on Lemma 10.39.15 in Commutative Algebra

This lemma does imply that faithful flatness can be lifted along nilpotent surjections . Flatness follows from lifting tor-amplitude which is documented elsewhere and faithfullness from the above. I couldn't find a reference elsewhere so perhaps it might be good to add it in this section.


On Charlotte left comment #10190 on Lemma 108.9.4 in Moduli Stacks

I NEED A CRYPTO RECOVERY EXPERT TO HELP ME RECOVER MY $142,OOO FROM SCAMMER

Good day Audience, I want to use this great medium to announce this information to the public about JETWEBHACKERS few months back, I was seeking an online BTC investment plan when I got scammed for about $142,000. I was so down and didn?t know what to do until I came across a timeline about JETWEBHACKERS, so I reached out to him and to my greatest surprise, they were able to recover all the funds which I had previously lost to the Devils. I am so glad to share this wonderful news with you all because it cost me nothing to announce a good and reliable Hacker as JETWEBHACKERS.

Reach out to them today and turn your situation around!

WEBSITE: jetwebhackers. com

EMAIL: jetwebhackers@gmail.com

Telegram: @jetwebhackers

WhatsApp: +1 (325) 721-3656


On W. Lee left comment #10189 on Lemma 10.138.16 in Commutative Algebra

minor typo, in the proof of Lemma 06CM, line -5, "Namely, is projective as a direct sum of the free module " is a direct summand of .


On W. Lee left comment #10188 on Lemma 10.138.16 in Commutative Algebra

minor typo, in the proof of Lemma 06CM, line -5, "Namely, is projective as a direct sum of the free module " is a direct summand of .


On Josh Park left comment #10187 on Section 2.5 in Conventions

some latex errors here?


On Josh Park left comment #10186 on Section 2.3 in Conventions

Agree with the initial comment here. Most undergraduate students with an interest in algebraic geometry have not encountered category theory and/or morphisms


On e.d. left comment #10185 on Section 5.26 in Topology

In Proposition 08YN, item (3) it is in fact to take a particular map Y-->Z of finite topological spaces where has 4 points, and has 3 points. This map happens to be surjective and proper, and the resulting lifting diagram is equivalent to Definition 5.26.1 without assuming anything about .

Would you consider adding this reformulation ? Perhaps this reformulation might clarify Definition 5.26.1 and "explain" use of surjectivity and compactness here to category-theoretically minded. I can spell out some details if you are interested.

Furthermore, one can reformulate Proposition 08YN and Lemma 090D in terms of weak factorisation systems cogenerated by surjective proper maps of finite topological spaces of size at most 7.


On David Holmes left comment #10184 on Section 37.53 in More on Morphisms

Chris: the fibres are stated to be (geometrically) connected, in particular they are non-empty.


On Chris left comment #10183 on Section 37.53 in More on Morphisms

Is there any reason the is not surjection in the Stein Factorization Theorems? It is not explicitly said, but certainly it must be?


On Reginald Anderson left comment #10182 on Section 59.6 in Étale Cohomology

Just a note on typesetting that there's a \PP^1_C in the exact sequence from the first paragraph where the subscript of C should be \mathbb{C} or whatever convention is used for \mathhbb{C} throughout.


On andy left comment #10181 on Section 15.42 in More on Algebra

Can I suggest to mention whether the property of being regular (all local rings are regular) ascends along regular maps here?


On left comment #10180 on Lemma 15.4.3 in More on Algebra

Perhaps after reading this article, you can gain more knowledge by reading the following articles. https://healthy-nature.tw/


On left comment #10179 on Lemma 15.4.3 in More on Algebra

Perhaps after reading this article, you can gain more knowledge by reading the following articles. https://healthy-nature.tw/


On left comment #10178 on Remark 13.19.5 in Derived Categories

This remark is a great illustration of how projective resolutions preserve morphism spaces under quasi-isomorphisms. A clear and elegant dual to the injective case—very helpful for understanding derived functors in practice kakahoki


On Shubhankar left comment #10177 on Lemma 10.133.3 in Commutative Algebra

Apologies if this is nonsense, but isn't there a universal differential operator ? As written the construction doesn't make this clear. Apologies again if I am mistaken or this is too trivial to make explicit.


On left comment #10176 on Lemma 13.20.1 in Derived Categories

For part (1), " computes..." should be replaced by " computes...".


On Haodong Yao left comment #10175 on Section 29.39 in Morphisms of Schemes

In the proof of Lemma 01VS, you write

"Hence they give rise to a morphism

but shortly after that you write , which should be as you denote the morphism by .