The Stacks project

Comments 521 to 540 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 #9199 on Lemma 10.115.3 in Commutative Algebra

I think the argument also works for .


On left comment #9198 on Lemma 92.5.8 in The Cotangent Complex

Thanks and fixed here.


On left comment #9197 on Section 20.28 in Cohomology of Sheaves

Thanks and fixed here.


On left comment #9196 on Section 105.7 in Introducing Algebraic Stacks

No problem!


On left comment #9195 on Lemma 9.16.6 in Fields

OK, yes this was a bit terse. I added a few sentences. Since this will be used only much later in the project, I think it can be a little bit less detailed than the rest of the chapter. Changes are here.


On left comment #9194 on Lemma 9.16.3 in Fields

And there was another typo too. Thanks and fixed here.


On left comment #9193 on Remark 10.78.4 in Commutative Algebra

Going to leave as is.


On left comment #9192 on Section 10.134 in Commutative Algebra

Thanks and fixed here.


On left comment #9191 on Section 26.21 in Schemes

@#9025. I do not understand, so I am going to leave this as is.


On left comment #9190 on Lemma 92.10.2 in The Cotangent Complex

Thanks and fixed here.


On left comment #9189 on Lemma 9.8.9 in Fields

Yes indeed. Thanks and fixed here.


On left comment #9188 on Lemma 59.73.13 in Étale Cohomology

THanks and fixed here.


On left comment #9187 on Lemma 10.63.4 in Commutative Algebra

I think the induction can start with . Going to leave as is.


On left comment #9186 on Lemma 10.62.2 in Commutative Algebra

Going to leave as is.


On left comment #9185 on Lemma 10.63.16 in Commutative Algebra

Thanks and fixed here.


On left comment #9184 on Lemma 10.43.6 in Commutative Algebra

Look, this is explained in the proof. Namely, in the first paragraph the extension is separable. By definition this means any finitely generated subextension is separably generated! Hence after replacing as in the proof, we may apply Lemma 10.42.3.


On left comment #9183 on Lemma 100.9.4 in Properties of Algebraic Stacks

Fixed here.


On left comment #9182 on Section 52.28 in Algebraic and Formal Geometry

Yes, very confusing. Thanks. Fixed here.


On left comment #9181 on Lemma 5.23.3 in Topology

Going to leave as is.


On left comment #9180 on Section 20.31 in Cohomology of Sheaves

Thanks and fixed by removing RHom here.