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 3693 in reverse chronological order.


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"


On slogan_bot left comment #3832 on Lemma 15.12.7 in More on Algebra

Suggested slogan: "Henselization commutes with base change along integral maps"


On slogan_bot left comment #3831 on Lemma 15.12.6 in More on Algebra

Suggested slogan: "The Henselization of a pair only depends on the radical of the ideal"


On slogan_bot left comment #3830 on Lemma 15.12.4 in More on Algebra

Suggested slogan: "Henselization of a Noetherian pair is Noetherian and does not affect completions"


On Antoine VEZIER left comment #3829 on Lemma 30.15.2 in Divisors

Small typo on line 5 I think. It is a_i, h\in A and not h_i, h\in A.


On Andy left comment #3827 on Section 10.85 in Commutative Algebra

For lemma 0597, shouldn't it be A' nonempty instead?


On Xiaofa Chen left comment #3824 on Section 12.9 in Homological Algebra

Yes. It's my mistake. At that time, I just learned this theory and I took it for granted that it is universal among all functors which annihilate . Then I realized that I is universal among exact functors which annihilate . And I don't know how to delete a 'stupid comment' as that.


On Kestutis Cesnavicius left comment #3823 on Lemma 15.81.5 in More on Algebra

The statement can evidently be strengthened to `if and only if'.


On Johannes Anschuetz left comment #3822 on Lemma 36.34.6 in More on Morphisms

The "Y" in the diagram seems to mean "S".


On slogan_bot left comment #3821 on Lemma 90.4.1 in Artin's axioms

Suggested slogan: Algebraic stacks satisfy the Rim-Schlessinger condition


On slogan_bot left comment #3820 on Lemma 36.2.5 in More on Morphisms

Suggested slogan: A composition of thickenings is a thickening


On slogan_bot left comment #3819 on Lemma 36.2.3 in More on Morphisms

Suggested slogan: Affineness is insensitive to thickenings


On Sandor Kovacs left comment #3818 on Lemma 10.118.2 in Commutative Algebra

At the end of the fourth paragraph (starting with "If then...") it should be saying that "R′/R is a finite R-module annihilated by a power of " not that "R′/R is a finite R-module annihilated by a power of x".


On Alapan Mukhopadhyay left comment #3817 on Lemma 10.98.1 in Commutative Algebra

In the diagram is to be replaced by .


On Manuel Hoff left comment #3816 on Section 28.24 in Morphisms of Schemes

Possible typo in Lemma 01U8. At one point I think it should say instead of .


On Kestutis Cesnavicius left comment #3815 on Lemma 28.40.1 in Morphisms of Schemes

Same comment as for https://stacks.math.columbia.edu/tag/01KE