The Stacks project

Comments 961 to 980 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 Alexis left comment #8736 on Section 10.39 in Commutative Algebra

For lemma 0BBY, you might also want that .

On Hayama Kazuma left comment #8735 on Lemma 33.37.6 in Varieties

In the proof, "Observe that ", here should be ?

On Eiki left comment #8734 on Section 60.13 in Crystalline Cohomology

Some possibly pedantic comments; "two ring maps " aren't they technically maps of sheaves where on the level of sections they are described as above?

If we are later calling to be the maps on the corresponding schemes, maybe we want to give it some other name (probably rather than here)?

On Hao left comment #8733 on Theorem 57.13.3 in Derived Categories of Varieties

Sorry I just found the answer that by \tag{0FDC} they are the same.

On Hao left comment #8732 on Theorem 57.13.3 in Derived Categories of Varieties

The original version in Orlov's paper concerns the coherent category, but the statement here is about perfect objects. Does this implies the coherent version? Or Does every fullly faithful embedding preserves perfect objects?

On Michael left comment #8731 on Section 39.7 in Groupoid Schemes

I am wondering about the small detail mentioned in Lemma 047S. Can someone explain it to me ?

On Kentaro Inoue left comment #8730 on Lemma 10.99.8 in Commutative Algebra

I think that this lemma can be proved more easily. In the first paragraph, (2) is proved in the case . In the general case, (2) can be reduced to the case by considering the -adic filtration. Then (1) follows from (2) immediately.

On Erhard Neher left comment #8729 on Lemma 8.10.6 in Stacks

Line 8 of the proof should read: We have to find a morphism restricting to ...

On Erhard Neher left comment #8728 on Lemma 8.10.1 in Stacks

Proof of (2), line (2): it should read instead of .

On Jim Davis left comment #8727 on Section 111.1 in Exercises

Exercise 078G. Replace idempotent by central idempotent

On Shiji Lyu left comment #8725 on Lemma 91.15.1 in Deformation Theory

In the second last paragraph, it looks like we should have , not . Am I right?

On Cameron Ruether left comment #8723 on Lemma 35.11.1 in Descent

Small typo, it seems points (3)-(6) should read "same as in (2)..."

On Roy Shtoyerman left comment #8722 on Definition 5.8.1 in Topology

It might be lacking a definition of an irreducible subset . I assume it's just irreducible as a space w.r.t. the subset topology, but it might be useful to elaborate for clarity.

On Eiki left comment #8721 on Section 60.7 in Crystalline Cohomology

In Definition 07I4, shouldn't it be if we are identifying the closed subscheme as a quasicoherent sheaf of ideals?

On Jiwan Jung left comment #8720 on Section 13.5 in Derived Categories

There are two different are used on the proof of 05R5. (one is g:X\rightarrow Y for assumption and the other is g:X\rightarrow Q for the choice of dtr.)

On Bjorn Poonen left comment #8719 on Section 15.8 in More on Algebra

Maybe add some easy but useful special cases to Lemma 07ZA:

One could add a new item "If is an ideal of , then ."

In (2), after "we have" and before the formula one could insert " and more generally" (I think that that is the most commonly used case of (2)).

In the proof of (4), it would be good to put in parentheses, twice.

On Keerthi Madapusi left comment #8718 on Lemma 75.21.1 in Derived Categories of Spaces

Looks like the reference in (2) is circular? Should probably replace 0DKG with 0DJ8?

On Laurent Moret-Bailly left comment #8717 on Lemma 15.121.1 in More on Algebra

@#8716: I think it suffices to substitute " in " in the penultimate sentence.

On Kentaro Inoue left comment #8716 on Lemma 15.121.1 in More on Algebra

I suspect that the argument in the last two sentences is not correct because does not necessary belong to . I think that it is easy to use the surjectivity of the map .

On Torsten left comment #8715 on Lemma 76.36.2 in More on Morphisms of Spaces

Is the condition that is affine really needed?


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