The Stacks project

Comments 1921 to 1940 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 #7647 on Lemma 45.11.2 in Weil Cohomology Theories

Thanks. Fixed here.


On left comment #7646 on Lemma 45.7.6 in Weil Cohomology Theories

It is indeed the case that sometimes the proofs in the Stacks project aren't trivial and the reader has to think a little bit. In this case I think the statement more or less tells you what to try.


On left comment #7645 on Section 27.17 in Constructions of Schemes

THanks fixed here.


On left comment #7644 on Lemma 20.15.1 in Cohomology of Sheaves

Thanks and fixed here.


On left comment #7643 on Lemma 37.17.3 in More on Morphisms

Thanks. Fixed here.


On left comment #7642 on Lemma 48.12.7 in Duality for Schemes

@#7499. Thanks for the typo. Fixed here.

@#7500. Yes, it does hold more generally. See Lemma 36.32.8 and use relative duality as discussed in this chapter.


On left comment #7641 on Definition 10.45.1 in Commutative Algebra

No.


On left comment #7640 on Lemma 33.44.6 in Varieties

@#7495: I don't agree with this.


On left comment #7639 on Lemma 28.25.3 in Properties of Schemes

THanks and fixed here.


On left comment #7638 on Lemma 33.43.2 in Varieties

Thanks to you all! See this commit.


On left comment #7637 on Lemma 36.8.1 in Derived Categories of Schemes

Thanks. Fixed here.


On left comment #7636 on Section 23.8 in Divided Power Algebra

OK, yes, very good. Please in the future leave the comment on the page of the proposition. Change is here.


On left comment #7635 on Lemma 53.3.2 in Algebraic Curves

THanks. Fixed here.


On left comment #7634 on Lemma 4.2.18 in Categories

Thanks. Fixed here.


On left comment #7633 on Section 21.36 in Cohomology on Sites

Thanks. Fixed here.


On left comment #7632 on Lemma 49.12.6 in Discriminants and Differents

Thanks and fixed.


On left comment #7631 on Definition 49.9.1 in Discriminants and Differents

Indeed! Thanks very much. Fix is here.


On left comment #7630 on Example 53.13.6 in Algebraic Curves

Indeed, thanks very much! Fixed here.


On left comment #7629 on Section 7.16 in Sites and Sheaves

Thanks. Fixed here.


On left comment #7628 on Definition 86.9.1 in Duality for Spaces

Yes, for any CM morphism (suitably defined -- not necessarily representable by algebraic spaces) between any algebraic stacks, you can define and construct a relative dualizing sheaf.