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\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 left comment #10055 on Section 15.1 in More on Algebra

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On José Burgos left comment #10054 on Lemma 40.14.10 in More on Groupoid Schemes

A typo: constuctible should be constructible


On Branislav Sobot left comment #10053 on Lemma 15.9.7 in More on Algebra

I believe this lemma is wrong as stated. I think you need an additional condition that and are at most the degree of . The counterexample I have in mind is: Take ring , , and .


On left comment #10052 on Proposition 15.48.7 in More on Algebra

In the last sentence of the proof of case (2), an explicit reference to Lemma 07P9 can improve the clarity.


On left comment #10051 on Lemma 15.48.6 in More on Algebra

I think replacing with also works, and it is better to say instead of .


On François Loeser left comment #10050 on Lemma 97.12.6 in Criteria for Representability

Line -2 : "is representable by an algebraic space over ", the use of here is confusing, since it has already another meaning. .


On Bach left comment #10049 on Definition 42.29.1 in Chow Homology and Chern Classes

Typo: "Given a integral". "a" should be changed to "an".


On Wenqi Li left comment #10048 on Section 15.101 in More on Algebra

Small typo: Before Lemma 15.101.5, above the commutative diagram, "for every we have ." A parenthesis is missing.


On left comment #10047 on Proposition 15.50.6 in More on Algebra

Lemma 045K can be cited at the end of the sentence "Thus we are done if the characteristic of is ".


On left comment #10046 on Lemma 15.48.5 in More on Algebra

Typo: should be .


On left comment #10045 on Section 3.8 in Set Theory

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On left comment #10044 on Lemma 15.46.4 in More on Algebra

There is an missing after "for every there exists a relation", i.e. it should be .


On Branislav Sobot left comment #10043 on Lemma 15.25.4 in More on Algebra

Sorry, you should really erase my comment(s)


On Branislav Sobot left comment #10042 on Lemma 15.25.4 in More on Algebra

I believe there is a typo in the statement. It should be "assume is a finite -module" not "-algebra"


On Pat Lank left comment #10041 on Lemma 53.24.1 in Algebraic Curves

There seems to be a missing period near the start of the statement: `... proper schemes over Assume ...'


On left comment #10040 on Proposition 10.162.15 in Commutative Algebra

Three comments on the proof:

  1. It seems that the reduction to being normal in Step 3 can be achieved at Step 5 (I do not see where normality of is needed until and including Step 5), i.e. Step 3 seems redudant.

  2. I agree with Jonas's comment.

  3. Two typos: "we have reduced to the proving the following" should be replaced with "we have reduced to proving the following" and "where the polynomial above split completely" should be replaced with "where the polynomial above splits completely".


On Aaron Jung left comment #10039 on Section 6.11 in Sheaves on Spaces

typo on Example007C,"if" of "In other words, an element if C∞Rn,x is ~" seems to mean "of".


On left comment #10038 on Lemma 10.41.5 in Commutative Algebra

I think that the argument by Ryo Suzuki \ref{https://stacks.math.columbia.edu/tag/00HY#comment-7873} is better since it shows that this is a purely topological statement: the image of a spectral map between spectral spaces is closed if and only if it is stable under specialization.


On Lei Y left comment #10037 on Section 48.4 in Duality for Schemes

In the first sentence "...the question to what extend" should be "...the question to what extent"


On Doug Liu left comment #10036 on Lemma 15.86.8 in More on Algebra

In the part "2 tags refer to this tag", 08U5 is missing.