The Stacks project

Comments 1761 to 1780 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 Zhiyu YUAN left comment #7822 on Section 11.3 in Brauer groups

What does to "view as an algebra" mean in the proof to Lemma 0745, i.e. over what field will be? Simply deleting this sentence seems to do no harm to the whole proof.

On Laurent Moret-Bailly left comment #7821 on Section 30.4 in Cohomology of Schemes

End of first sentence of section: "are zero".

On Que left comment #7820 on Section 60.4 in Crystalline Cohomology

minor typo: insure -> ensure

On Xiaolong Liu left comment #7819 on Lemma 33.15.1 in Varieties

We may should remove the single quotation mark in the third sentence of the second paragraph.

On Jinyong An left comment #7817 on Definition 5.10.5 in Topology

For the definition of equidimensional topological space, it allows that each irreducible components has same dimension of infinity? Or, finiteness of each (same) dimension of the irreducible components is required?

On Verroq left comment #7816 on Section 39.4 in Groupoid Schemes

Typo in the Diagram under Def 022S: On the right arrow, it should be m', not m.

On Anonymous left comment #7815 on Lemma 13.28.5 in Derived Categories

Should the lemma say instead that the composition is the identity map? Or is the first map not the map ?

On Anonymous left comment #7814 on Lemma 13.16.3 in Derived Categories

In the second sentence of the second paragraph of the proof, I think it should read "... we obtain a distinguished triangle ... in " instead of "... we obtain a distinguished triangle ... in ".

On left comment #7812 on Lemma 59.77.3 in Étale Cohomology

For quasi-compact spaces, being locally finite tor dimension is the same as having finite tor dimension. Maybe this should be explained in Section 21.46 as well.

On R left comment #7811 on Lemma 59.77.3 in Étale Cohomology

The hypothesis is that has locally finite tor dimension, but you seem to use (and prove) that has finite tor dimension. Are they equivalent in this case? (If I understand correctly, Tag 21.46.5 shows that finite tor dimension implies locally finite tor dimension, though this is never spelled out.)

On Raffaele Lamagna left comment #7810 on Proposition 15.78.3 in More on Algebra

Typo: I think that in the definition of should be

On Peng Du left comment #7809 on Lemma 49.11.7 in Discriminants and Differents

I think in condition (1), it needs add that U=Spec(A)⊂X is an (affine) open neighbourhood of x.

On Peng Du left comment #7808 on Remark 49.11.6 in Discriminants and Differents

Change "After a change of coordinates with may assume" to "After a change of coordinates we may assume".

On Peng Du left comment #7807 on Lemma 49.11.5 in Discriminants and Differents

Needs a period at the end of statement.

On David Liu left comment #7806 on Section 29.39 in Morphisms of Schemes

Lemma 29.39.8. : The last line : , should it be ?

On left comment #7805 on Section 37.16 in More on Morphisms

Because French is better? No, it's just that I love saying that phrase. Is that OK? Please feel free to complain!

On left comment #7804 on Section 29.8 in Morphisms of Schemes

I guess my pedantic reply would be: what is a schematically dense subset? Anyway, if I read it as just a "dense subset" then the inclusion of the generic point of a variety would not be a dominant morphism (in general). So I think that would be very different for morphisms of general schemes. For a morphism between varieties, it would give the same notion.

On left comment #7803 on Lemma 66.21.4 in Properties of Algebraic Spaces

You use Remark 66.7.6 which in tern uses the preceding Definition 66.7.5 to define what this means. So it makes sense even if the local ring does not make sense. OK?

On Nicolás left comment #7802 on Definition 13.41.1 in Derived Categories

It seems that (2) is missing an explicit mention of the inductive construction, as it is not specified which morphism are we working with. Something like "If , then it is a choice of a Postnikov system for and a choice of a distinguished [...]." (And probably, in that case (2) and (3) could be unified.)

On 羽山籍真 left comment #7801 on Lemma 66.21.4 in Properties of Algebraic Spaces

I would like to ask where the notion "local rings" is defined for general algebraic space, since (2) used this (maybe it would be nice if we recall it here). I only know that for decent algebraic space we have Henselian local rings and for geometric points on general algebraic space we have strict Henselian local rings...


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