The Stacks project

Comments 1 to 20 out of 7282 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 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 65.21.4 in Properties of Algebraic Spaces

You use Remark 65.7.6 which in tern uses the preceding Definition 65.7.5 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 65.21.4 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...

On Jonas Ehrhard left comment #7800 on Lemma 33.39.5 in Varieties

Dieudonne's Topics in Local Algebra contains the statement that is the integral closure of in its total ring of quotient for a reduced noetherian G-ring of arbitrary dimension (Theorem 6.5 ib.). Is there something comparable in the stacks-project?

On Xiaolong Liu left comment #7799 on Lemma 10.128.1 in Commutative Algebra

One should repalce '' by ''.

On Anonymous left comment #7798 on Lemma 13.9.5 in Derived Categories

In the lemma statement, should "If is a split surjection" instead read "If is a termwise split surjection" ?

On Ravi Vakil left comment #7797 on Section 29.8 in Morphisms of Schemes

I have a question, from an interesting comment by Hikari Iwasaki. What about "dominant" defined to mean "the preimage of a schematically dense subset is always schematically dense"?

On Laurent Moret-Bailly left comment #7792 on Proposition 98.8.4 in Quot and Hilbert Spaces

In the proof, the "coherent sheaf " is only quasi-coherent of finite presentation.

On Heiko Braun left comment #7791 on Lemma 13.30.1 in Derived Categories

typo: "an s" in the first line of the proof

On Jakob Werner left comment #7790 on Lemma 20.11.4 in Cohomology of Sheaves

In the displayed equation of the proof, the index should be a .

On left comment #7789 on Equation in Commutative Algebra

Yes, but for technical reasons it's currently not a link (nor is it possible to toggle the tag to be a number).

On left comment #7788 on Equation in Commutative Algebra

On the right hand side, the subscript should likely refer to tag 051U instead of being simply "(051U)"

On Bogdan left comment #7787 on Lemma 59.97.2 in Étale Cohomology

Is it clear that the isomorphism constructed in the proof coincides with the morphism induced by the cup product?