The Stacks project

Comments 421 to 440 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 #9301 on Lemma 48.15.1 in Duality for Schemes

Indeed. Weakend assumptions here.


On left comment #9300 on Section 63.1 in More Étale Cohomology

this.


On left comment #9299 on Lemma 43.17.2 in Intersection Theory

Good catch! Fixed here.


On left comment #9298 on Section 17.26 in Sheaves of Modules

Thanks and fixed here.


On left comment #9297 on Lemma 12.6.3 in Homological Algebra

Thanks for the references. Going to leave as is.


On left comment #9296 on Lemma 10.157.3 in Commutative Algebra

Thanks and fixed here.


On left comment #9295 on Lemma 13.27.7 in Derived Categories

Thanks for the typo. I added a description of the composition law on Ext groups. See this commit.


On left comment #9294 on Section 59.33 in Étale Cohomology

Oops. Fixed here.


On left comment #9293 on Section 10.63 in Commutative Algebra

No: the annihilator of in is not a prime ideal.


On left comment #9292 on Lemma 76.14.3 in More on Morphisms of Spaces

Thanks and fixed here.


On left comment #9291 on Section 28.16 in Properties of Schemes

Thanks and fixed here.


On left comment #9290 on Section 42.44 in Chow Homology and Chern Classes

See Definition 42.7.6.


On left comment #9289 on Lemma 15.83.8 in More on Algebra

OK, this is such a technical lemma that a slogan does not work well, I think.

I like your and Yuchen Wu's suggestion of the additional lemma. I have added it here.


On left comment #9288 on Section 6.17 in Sheaves on Spaces

Those two sentences look fine to me. What exactly is confusing there?


On left comment #9287 on Section 5.21 in Topology

Thanks. I tried to add your proofs, but I found myself editing quite a bit... See changes here.


On left comment #9286 on Proposition 96.14.3 in Sheaves on Algebraic Stacks

Thanks and fixed here.


On left comment #9285 on Lemma 38.10.9 in More on Flatness

First, in your argument, I would prefer using Lemma 10.5 (the one we're commenting on) instead of Proposition 38.10.3.

The reason I don't want to add this, is that it is sort of the wrong thing to ask for: one should ask for the module to be "relatively finitely presented" with respect to . But we haven't introduced this notion for local homomorphisms of local rings which are essentially of finite type.

This is alluded to in the discussion following Definition 38.4.1. There it is also mentioned that we'll work around this as needed. So if we ever need what your (short) argument shows, then we'll just insert that argument where needed.

Finally, in case we have Lemma 38.10.10.


On left comment #9284 on Lemma 5.8.17 in Topology

No because in the Stacks project, connected spaces are nonempty, see Definition 5.7.1.


On left comment #9283 on Section 49.15 in Discriminants and Differents

I am quite sure that Lemma 49.15.1 is correct.


On left comment #9282 on Remark 50.12.2 in de Rham Cohomology

Thanks and fixed here.