The Stacks project

Comments 1441 to 1460 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 #8192 on Remark 42.56.8 in Chow Homology and Chern Classes

WhyFiniteDimension indeed! This led to some slight improvements also in later results, for example Proposition 42.57.1. Thanks! Changes are here.

On left comment #8191 on Section 110.19 in Examples

Thanks and fixed here.

On left comment #8190 on Lemma 107.5.18 in The Geometry of Algebraic Stacks

Thanks R! Fixed here.

On left comment #8189 on Lemma 27.15.5 in Constructions of Schemes

It is defined in the sense that is a graded ring and is the th graded part of this ring.

On left comment #8188 on Lemma 59.75.6 in Étale Cohomology

Thanks! Those would indeed be statements we could add in other lemmas. One of the uses of this lemma is to show something is constructible. And in the treatment of constructible sheaves in the Stacks project we have, for better or worse, assumed the coefficient ring is Noetherian. Thus we cannot even make the statement (for constructible guys) you are talking about without a significant revision of all of this material. So I will leave this for now.

On left comment #8187 on Lemma 54.4.3 in Resolution of Surfaces

Thanks and fixed here.

On left comment #8186 on Lemma 54.4.1 in Resolution of Surfaces

Thanks and fixed here.

On left comment #8185 on Lemma 48.27.1 in Duality for Schemes

Thanks, yes, already fixed here.

On left comment #8184 on Lemma 42.46.2 in Chow Homology and Chern Classes

Indeed, thank you. Fixed here.

On left comment #8183 on Lemma 33.35.3 in Varieties

Well, hmm, the notation isn't great, but I think that during th proof we think of the -vector space as given by the set of all vectors . Similarly, the notation is meant to indicate the -dimensional space of linear functions parametrized by vectors . Then the notation is intended as the subvector space of this. OK?

On left comment #8182 on Theorem 89.8.3 in Resolution of Surfaces Revisited

Thanks and fixed here.

On left comment #8181 on Lemma 31.9.6 in Divisors

Thanks and fixed here.

On left comment #8180 on Lemma 87.35.3 in Formal Algebraic Spaces

Thanks and fixed here.

On left comment #8179 on Lemma 42.41.4 in Chow Homology and Chern Classes

The notation has only been defined for ample , see Definition 33.45.10.

On left comment #8178 on Section 20.27 in Cohomology of Sheaves

Thanks and fixed here.

On left comment #8177 on Section 15.73 in More on Algebra

This section is just about constructing the maps. In future sections we prove some of these maps are isomorphisms. See for example: Sections 15.98 and 15.99.

On left comment #8176 on Lemma 37.2.3 in More on Morphisms

Your reference is for the finite order thickening case. I have added it here.

On left comment #8175 on Lemma 15.91.23 in More on Algebra

No (and no).

On left comment #8174 on Section 15.68 in More on Algebra

Thanks and fixed here.

On left comment #8173 on Definition 10.96.2 in Commutative Algebra

OK, I changed this but I think sometimes people use to indicate the zero module. This sort of makes sense if you think of as the ideal generated by in the ring . See this commit.


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