The Stacks project

\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*}

Comments 1 to 20 out of 3708 in reverse chronological order.


On Luke left comment #3884 on Equation 87.4.0.1 in Examples of Stacks

Typo: It should be instead of the other direction and the refering of f-maps is also unnecessary.


On slogan_bot left comment #3863 on Proposition 53.26.4 in Fundamental Groups of Schemes

Suggested slogan: "Ramanujam--Samuel for finite étale covers."


On anon left comment #3862 on Lemma 10.106.6 in Commutative Algebra

Why does surjective imply finite? Perhaps the finiteness should be an apriori assumption?


On anon left comment #3861 on Lemma 10.106.6 in Commutative Algebra

Why does surjective imply finite? Perhaps the finiteness should be an apriori assumption?


On Emmanuel Kowalski left comment #3859 on Section 54.65 in √Čtale Cohomology

Is the French title intentional?


On Alice left comment #3856 on Lemma 10.50.4 in Commutative Algebra

While minor, It would be better to simply say , insteady of the roundabout . Also a note, the only point where locality is used is to guarente for all I for nakayama's lemma, so this can be generalised very easily if so desired.


On Zhiyu Zhang left comment #3854 on Lemma 15.30.4 in More on Algebra

Maybe a little type: "Set " shall be "Set ".


On Matthieu Romagny left comment #3853 on Section 35.16 in Derived Categories of Schemes

Missing 's' in third sentence: hence these do not give perfect objects


On Matthieu Romagny left comment #3852 on Section 30.10 in Divisors

Typo in third sentence of this section: it is useful to have a canonical closed subscheme


On Lucy left comment #3850 on Section 10.19 in Commutative Algebra

In the proof of Nakayama's Lemma, lemma 10.16.2 is referred, but it seems that lemma 10.18.1 is a better choice.


On Marco left comment #3848 on Section 36.2 in More on Morphisms

Hi, I think the indexation after "filtered by closed subspaces" is not correct. After there is . I think it should be .


On Victoria Mitchell left comment #3847 on Section 10.4 in Commutative Algebra

This is a minor change, but it would be ungrammatical to say "Suppose given a commutative diagram ..., then there is a canonical exact sequence ..."; rather, this should say "Suppose [we are] given a commutative diagram ... of abelian groups with exact rows, then there is a canonical exact sequence ..."


On Laurent Moret-Bailly left comment #3844 on Lemma 12.5.11 in Homological Algebra

@Junho Won: no. For instance, if , the diagram is cocartesian for any .


On Junho Won left comment #3843 on Lemma 12.5.11 in Homological Algebra

I think the second exact sequence is missing a 0 on the left.


On Rene left comment #3840 on Definition 7.38.1 in Sites and Sheaves

Maybe it should be clarified if 'family of points' means 'set of points'


On slogan_bot left comment #3839 on Lemma 25.23.6 in Schemes

Suggested slogan: "Any injective on topological spaces map of schemes is separated."


On Yuxuan left comment #3838 on Section 42.6 in Intersection Theory

You missed a \dim (f(Z)).


On anonymous left comment #3837 on Lemma 26.4.1 in Constructions of Schemes

This refers to Tag 01LR just above. It seems that the f on the right hand side should be the morphism making T into an S-scheme. So my suggestion is to write \phi. (The right hand side should be in "set brackets" but it did not work in the preview.) In the representability statements below it would be good to say representable by an S-scheme.


On slogan_bot left comment #3836 on Lemma 57.13.1 in Algebraic Spaces

Suggested slogan: "The diagonal of any algebraic space is a separated, locally quasi-finite monomorphism"


On slogan_bot left comment #3833 on Lemma 28.24.15 in Morphisms of Schemes

Suggested slogan: "Schme theoretic image of a quasi-compact morphism commutes with flat base change"