The Stacks project

Comments 1581 to 1600 out of 9050 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 left comment #8039 on Lemma 49.11.7 in Discriminants and Differents

Very good. Fixed here.


On left comment #8038 on Remark 49.11.6 in Discriminants and Differents

Thanks and fixed here.


On left comment #8037 on Lemma 49.11.5 in Discriminants and Differents

Thanks and fixed here.


On left comment #8036 on Section 29.39 in Morphisms of Schemes

Thanks and fixed here.


On left comment #8035 on Definition 13.41.1 in Derived Categories

Thanks and fixed here.


On François Loeser left comment #8034 on Lemma 19.12.1 in Injectives

There is a typo on line 3: should be


On left comment #8033 on Lemma 33.39.5 in Varieties

No, I don't think so for the moment.


On left comment #8032 on Lemma 10.128.1 in Commutative Algebra

Thanks and fixed here.


On left comment #8031 on Lemma 13.9.5 in Derived Categories

Thanks again Anonymous! Fixed here.


On left comment #8030 on Proposition 99.8.4 in Quot and Hilbert Spaces

Thanks. I lazily fixed this by just saying module. The reader has to check that it is indeed something that gives an object of the stack Coh. See this.


On left comment #8029 on Lemma 13.30.1 in Derived Categories

Thanks and fixed here.


On left comment #8028 on Lemma 20.11.4 in Cohomology of Sheaves

Thanks and fixed here.


On left comment #8027 on Lemma 59.97.2 in Étale Cohomology

First of all, yes. But I think you are saying that we didn't write out the proof of this fact. And you would be right about that. This issue comes up in several guises in discussing variants of Kunneth, for example, see proof of Lemma 33.29.2. We should try to come up with a suitably general discussion that allows us to prove these maps agree in many different settings.


On left comment #8026 on Definition 68.11.5 in Decent Algebraic Spaces

Very good! Thanks and fixed here.


On left comment #8025 on Lemma 10.160.6 in Commutative Algebra

Dear Juhani, thank you for mentioning this.


On left comment #8024 on Lemma 10.114.1 in Commutative Algebra

Leaving this as is. General comments: We do need many, many more (counter) examples. We have a chapter for that, but we should also think about how to sort of point back an forth to results.


On left comment #8023 on Lemma 81.3.2 in Pushouts of Algebraic Spaces

Yes, I agree. But will this ever be useful? Going to leave as is for now.


On left comment #8022 on Definition 15.36.1 in More on Algebra

Thanks and fixed here.


On left comment #8021 on Section 81.11 in Pushouts of Algebraic Spaces

Thanks and fixed here.


On left comment #8020 on Section 59.12 in Étale Cohomology

Thanks and fixed here.