The Stacks project

Comments 781 to 800 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 #8932 on Lemma 15.41.3 in More on Algebra

Why not just quote this lemma and Lemma 15.41.2 if you need base change by a ring map which is essentially of finite type.


On left comment #8931 on Lemma 15.41.7 in More on Algebra

Going to leave as is.


On left comment #8930 on Lemma 10.34.2 in Commutative Algebra

Dear William, I note that the first step of your proof uses the Hilbert Nullstellensatz (unless I am overlooking something). Now our proof of the Nullstellensatz already uses Chevalley. So this wouldn't avoid using Chevalley. Additionally, there is a step in your proof which uses a lemma that comes after this one, so we can't use that here.


On left comment #8929 on Section 37.21 in More on Morphisms

Thanks and fixed here.


On left comment #8928 on Section 64.16 in The Trace Formula

Thanks and fixed here.


On left comment #8927 on Section 4.15 in Categories

Sure.


On left comment #8926 on Definition 64.14.2 in The Trace Formula

Thanks and fixed here.


On left comment #8925 on Definition 64.8.1 in The Trace Formula

Thanks and fixed here.


On left comment #8924 on Lemma 64.7.2 in The Trace Formula

Thanks and fixed here.


On left comment #8923 on Lemma 10.143.8 in Commutative Algebra

Thanks and fixed here.


On left comment #8922 on Section 13.34 in Derived Categories

OK, I fixed this in the opposite way, because actually to prove the "canonicity" would be quite annoying. So I fixed it by making the map maximally noncanonical. See somewhat large set of changes here.


On left comment #8921 on Section 110.6 in Examples

OK, it would take too much time for me to write this out in detail, so I will not add this for now. If anybody wants to contribute this, please send me some latex with details.


On left comment #8920 on Lemma 36.5.4 in Derived Categories of Schemes

Thanks and fixed here.


On left comment #8919 on Subsection 112.5.2 in A Guide to the Literature

See this page.


On left comment #8918 on Section 23.7 in Divided Power Algebra

Fixed the typo here.


On left comment #8917 on Proposition 59.95.6 in Étale Cohomology

Thanks and fixed here.


On left comment #8916 on Section 50.7 in de Rham Cohomology

Thanks and fixed here.


On left comment #8915 on Lemma 4.22.9 in Categories

OK, I upgraded this lemma to deal with the use case you mentioned and I fixed the proof in derived categories as you suggested. It still isn't optimal perhaps because it could be formulated on the level of functors, but we can add that if we ever need it. Thanks! Changes are here.


On left comment #8914 on Lemma 33.7.10 in Varieties

What you say works, but that is not how I think about it. If you have a as in the lemma, then is the image of . So really one is just checking that the image of is closed in which may be done locally.

I am going to leave as is for now.


On left comment #8913 on Lemma 15.114.4 in More on Algebra

Thanks and fixed here.