The Stacks project

Comments 1541 to 1560 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 #8081 on Lemma 39.9.10 in Groupoid Schemes

Thanks and fixed here.

On left comment #8080 on Section 48.2 in Duality for Schemes

Please always comment on the page of the tag you are commenting on. Thanks. Fixed here.

On left comment #8079 on Section 12.15 in Homological Algebra

Not going to do this. The thing with the short exact sequence is explained in Remark 13.12.4; as you can see we just use for the thing that fits into the ses.

Other people have mentioned they prefer to use superscripts, so use and when using truncation functors for complexes with upper numbering (so for cochain complexes). If you read this and have an opinion, please leave a comment.

On left comment #8078 on Lemma 15.41.4 in More on Algebra

Thanks and fixed here.

On left comment #8077 on Section 44.6 in Picard Schemes of Curves

Thanks and fixed here.

On Laurent Moret-Bailly left comment #8076 on Lemma 37.26.6 in More on Morphisms

First line of proof: should be . But in fact it is not very clear whether one is proving that is reduced or that is. I propose to change the first 3 lines as follows:

Assume the special fibre is reduced. Let be any point, and let us show that
is reduced. (This will prove that and are reduced). Let be a specialization with in the special fibre; such a specialization exists as a proper morphism is closed. Consider the local ring . Then is a localization of , so it suffices to show that is reduced. Let be a uniformizer. (The rest is unchanged)

On left comment #8075 on Lemma 101.45.7 in Morphisms of Algebraic Stacks

THanks and fixed here.

On left comment #8074 on Lemma 15.124.1 in More on Algebra

Thanks and fixed here.

On left comment #8073 on Section 12.19 in Homological Algebra

Please comment on each of the items separately (on the page of the tag itself) and tell me exactly what to fix.

On left comment #8072 on Lemma 15.64.2 in More on Algebra

Thanks and fixed here.

On left comment #8071 on Definition 12.31.2 in Homological Algebra

Yes, I am confused too. THanks for catching this. I have fixed it and made the discussion slightly more precise here.

On left comment #8070 on Section 26.14 in Schemes

Going to leave this as is for now (one need to say what the map is when talking about the quotient topology).

On left comment #8069 on Section 59.46 in Étale Cohomology

Thanks and fixed here.

On left comment #8068 on Section 9.10 in Fields

Thanks and fixed here.

On left comment #8067 on Section 71.13 in Divisors on Algebraic Spaces

Thanks and fixed here.

On left comment #8066 on Section 17.7 in Sheaves of Modules

Thanks and fixed here. If you wanted to be listed as a contributor can you (re)confirm your name?

On left comment #8065 on Section 12.3 in Homological Algebra

Somebody else can write this up (also look at the comment of bouthier on Section 12.4). Please coordinate with me.

On left comment #8064 on Example 12.3.13 in Homological Algebra

The category of filtered vector spaces has kernels and cokernels but is not abelian. So it is interesting in that it shows one needs the Im Coim axiom.

On left comment #8063 on Lemma 33.47.1 in Varieties

Fixed here.

On left comment #8062 on Definition 39.9.1 in Groupoid Schemes

Thanks! I've added this as a remark. See this.


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