The Stacks project

Comments 1 to 20 out of 4550 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 Peng DU left comment #4893 on Lemma 42.12.2 in Chow Homology and Chern Classes

In line 3 and 7 of the proof, the term (f∘g)∗[W] should be (g∘f)∗[W].


On Spencer Dembner left comment #4892 on Section 9.25 in Fields

Does the sentence beginning "By linear algebra..." get used? It seems like everything used later in the proof follows from the minimal polynomial fact alone.


On Peng DU left comment #4891 on Section 42.33 in Chow Homology and Chern Classes

Maybe it's better to change "chern" to "Chern" everywhere (I find quite a few "chern" in titles of sections in this chapter).


On Rankeya left comment #4890 on Lemma 10.126.1 in Commutative Algebra

First sentence of proof should say: The category is non-empty as is an object of it.


On SDIGR left comment #4889 on Lemma 98.27.7 in Morphisms of Algebraic Stacks

Typo: "Note that is..." should be "Note that is..."


On SDIGR left comment #4888 on Lemma 98.27.7 in Morphisms of Algebraic Stacks

Typo: "Note that is..." should be "Note that is..."


On Peng DU left comment #4887 on Lemma 10.51.10 in Commutative Algebra

Need assume .


On QGravity left comment #4886 on Section 53.9 in Algebraic Curves

Does the genus of the curve in fix the equation of the curve uniquely? Could you please add references for the curves in ?


On Manuel Hoff left comment #4885 on Lemma 10.40.10 in Commutative Algebra

Small typo: In the first sentence of the proof, .


On Matt Larson left comment #4884 on Lemma 50.11.4 in de Rham Cohomology

I think it should say "In this way we see that is a free -module...".


On Rankeya left comment #4883 on Lemma 10.136.4 in Commutative Algebra

Suggested slogan: Smoothness is preserved under base change.


On left comment #4881 on Section 98.18 in Morphisms of Algebraic Stacks

There seems to be a small typo in the subscript of the union in Lemma 06FZ, where should be replaced by .


On left comment #4880 on Section 64.3 in Morphisms of Algebraic Spaces

Condition (2) in the third line of this section, 'fppf local on the base', seems to be hyperlinked to the wrong place only when I download the pdf. It works well on the website, but on the pdf the link sends me to Lemma 03MU, about universal injectiveness, whereas it should send me to Definition 02KO.


On left comment #4879 on Lemma 10.51.5 in Commutative Algebra

But is assumed to be an -module so the kernel of already annihilates all of .


On Peng DU left comment #4878 on Lemma 10.51.5 in Commutative Algebra

In the proof, it says "And if R→S is surjective, then any R-submodule of M is automatically an S-submodule", but I think that may need to assume the kernel of R→S kills the submodule N: (otherwise, take bigger thant and , then we can't make N an S-submodule of M).


On Adrian left comment #4877 on Section 95.9 in Artin's Axioms

In Definition 95.9.1, the horizontal arrows in the diagram are reversed.


On HAO left comment #4876 on Lemma 10.148.7 in Commutative Algebra

Sorry but I can't see why Lemma 10.121.1 is needed in the proof of Lemma 10.148.7. Where did you use ?


On left comment #4875 on Section 91.13 in Algebraic Stacks

Minor typo: in the proof of Lemma 03YS, it should say 'We may think of this as a surjective étale morphism of algebraic spaces'.


On left comment #4874 on Section 8.7 in Stacks

In Lemma 036Y, statements (2) and (3), the condition should be that and are stacks in groupoids/setoids over , not over .


On left comment #4873 on Section 91.11 in Algebraic Stacks

In condition (1) there seems to be a small typo, where should be replaced by .