The Stacks project

Comments 581 to 600 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 #9139 on Lemma 28.26.14 in Properties of Schemes

Thanks for your question which I addressed here.


On left comment #9138 on Lemma 10.143.4 in Commutative Algebra

OK, I changed 2 but not 1. See here.


On left comment #9137 on Lemma 12.8.1 in Homological Algebra

Thanks and added here.


On left comment #9136 on Lemma 37.62.1 in More on Morphisms

Thanks and fixed here.


On left comment #9135 on Remark 13.36.7 in Derived Categories

Thanks and fixed here.


On left comment #9134 on Proposition 10.138.8 in Commutative Algebra

Thanks and fixed here.


On left comment #9133 on Lemma 10.140.9 in Commutative Algebra

Well, I agree that you can use Lemma 10.137.17, but I think Lemma 10.137.18 is appropriate here as well. I'm going to leave this as is for now.


On left comment #9132 on Section 34.7 in Topologies on Schemes

Thanks and fixed here.


On left comment #9131 on Section 12.28 in Homological Algebra

Yep. Fixed here.


On left comment #9130 on Lemma 26.2.2 in Schemes

Thanks and fixed here.


On left comment #9129 on Definition 38.34.11 in More on Flatness

Thanks and fixed here.


On left comment #9128 on Lemma 78.19.6 in Groupoids in Algebraic Spaces

Good catch! Thanks very much. Fixed here.


On left comment #9127 on Lemma 37.64.2 in More on Morphisms

This was just silly. It's really quite elementary. I have improved it here.


On left comment #9126 on Section 10.90 in Commutative Algebra

Thanks and fixed here.


On left comment #9125 on Section 61.5 in Pro-étale Cohomology

Thanks and fixed here.


On left comment #9124 on Section 43.7 in Intersection Theory

Thanks and fixed here.


On left comment #9123 on Lemma 60.21.2 in Crystalline Cohomology

No, this is correct as stated. For one gets the cohomology of which can be very interesting for any value of !


On left comment #9121 on Lemma 59.65.2 in Étale Cohomology

No. The issue is that an infinite direct sum of locally constant sheaves needn't be locally constant, whereas that is the case for modules endowed with continuous action. An example would be to consider the direct sum of for all on . There is no single etale covering that trivializes this thing.


On left comment #9120 on Lemma 28.22.3 in Properties of Schemes

Going to leave as is. We often use the results stated in Section 26.24 without mention.


On left comment #9119 on Lemma 31.15.7 in Divisors

Thanks and fixed here.