The Stacks project

Comments 341 to 360 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 #9382 on Section 35.8 in Descent

Thanks and fixed here.


On left comment #9381 on Lemma 18.34.3 in Modules on Sites

Thanks and fixed here.


On left comment #9380 on Lemma 15.22.11 in More on Algebra

Thanks and fixed here.


On left comment #9379 on Lemma 36.13.4 in Derived Categories of Schemes

Yes, but we already have Lemma 36.13.5 which I move to this location in this commit.


On left comment #9378 on Lemma 36.13.6 in Derived Categories of Schemes

Thanks and fixed here.


On left comment #9377 on Lemma 29.54.4 in Morphisms of Schemes

Sounds good (I didn't check the Bourbaki reference). The intersections are potentially over infinite sets of points, so difficult to work with in general. I am going to leave this alone until we need it for another statement in the Stacks project.


On left comment #9376 on Section 60.5 in Crystalline Cohomology

Thanks and fixed here.


On left comment #9375 on Section 60.6 in Crystalline Cohomology

Thanks and fixed here.


On left comment #9374 on Lemma 21.47.3 in Cohomology on Sites

Thanks and fixed here.


On left comment #9373 on Section 73.9 in Topologies on Algebraic Spaces

Thanks and fixed here.


On left comment #9372 on Section 19.10 in Injectives

For those whose browser does not compile well the LaTeX in comment #2391 (like mine), you may find #2391 in plain text here.

@#2315 A proof of the equivalence between definitions of the AB5 condition is N. Popescu, Abelian Categories with Applications to Rings and Modules, Sect. 2.8, Theorem 8.6.

In case it is interesting to point this out: AB5 implies AB4 as it is currently stated in 19.10.1. A reference is ibid., Theorem 8.8.


On Hsueh-Yung left comment #9371 on Lemma 10.153.9 in Commutative Algebra

A typo just after the displayed formula: it should be .


On left comment #9370 on Section 38.32 in More on Flatness

@#8700 If I understand correctly, then no.


On left comment #9369 on Section 17.16 in Sheaves of Modules

Going to leave as is.


On left comment #9368 on Lemma 31.23.8 in Divisors

Thanks for the typo. Fixed here. Leaving the rest alone.


On left comment #9367 on Theorem 15.90.16 in More on Algebra

Thanks for pointing this out! The functors Can and are adjoint which is why it works; I guess this was at the back of my mind when I wrote this. See changes here.


On left comment #9366 on Section 10.106 in Commutative Algebra

Thanks and fixed here.


On left comment #9365 on Example 15.62.4 in More on Algebra

Thanks and fixed here.


On left comment #9364 on Lemma 107.5.22 in The Geometry of Algebraic Stacks

Yes. This term hasn't been defined in the Stacks project and I think we shouldn't. So the fix would be to restate in full the condition intended in each instance. I also think some more work could be done on this chapter, e.g., to shorten proofs (by splitting out lemmas for example). Going to leave this as is for now.


On left comment #9363 on Proposition 10.89.3 in Commutative Algebra

Going to leave as is.