Recent comments—The Stacks project

Comments 1 to 20 out of 8057 in reverse chronological order.

On Sep 21, 2023 Matthew left comment #8672 on Section 12.3 in Homological Algebra

@#8671 No, simple misread on my part.

On Sep 21, 2023 Matthew left comment #8671 on Section 12.3 in Homological Algebra

In the proof of Lemma 12.3.4: "It follows that $i \circ p + j \circ q : z \to z$ is the identity since..."

I think that this should read "It follows that $p \circ i + q \circ j : z \to z$ is the identity since..." Otherwise the map in question is not well-defined. The rest of the argument works fine.

On Sep 19, 2023 Sveta M left comment #8670 on Lemma 50.24.2 in de Rham Cohomology

Typo: "In Situation 0G8G the psuhforward" should be "... pushforward".

On Sep 19, 2023 Sveta M left comment #8669 on Lemma 50.24.2 in de Rham Cohomology

Typo: "In Situation 0G8G the psuhforward" should be "... pushforward".

On Sep 19, 2023 Sveta M left comment #8668 on Lemma 50.24.2 in de Rham Cohomology

Typo: "In Situation 0G8G the psuhforward" should be "... pushforward".

On Sep 17, 2023 Johan left comment #8667 on Lemma 34.9.2 in Topologies on Schemes

Ah, yes, of course. Silly me! I will add this as an example soon.

On Sep 13, 2023 Sa'ar Zehavi left comment #8666 on Section 55.8 in Semistable Reduction

In Lemma 0CD9, it seems that there is a redundant condition that $H^0(C,\mathcal{O}_C) = K$ . If $C$ is a projective curve, it is proper. In Tag 0A22, a curve $C/K$ is defined to be a variety of dimension 1 relative to $K$ , and is therefore, in particular irreducible. An irreducible proper scheme has only trivial sections, hence the condition $H^0(C,\mathcal{O}_C) = K$ is redundant. Am I missing anything?

On Sep 13, 2023 KrLee left comment #8665 on Section 43.18 in Intersection Theory

A typo: The dimension of $V$ should be $r$ instead of $s$ in lemma 0B0S.

On Sep 10, 2023 Owen B left comment #8664 on Section 15.52 in More on Algebra

it might be worth noting that the properties of excellence and quasi-excellence can be checked zariski-locally

On Sep 10, 2023 Alexis left comment #8663 on Section 35.34 in Descent

In the definition of the descent data 023V, the same notation is used for the morphism $f:X\rightarrow S$ and the morphism of descent data.

On Sep 07, 2023 Andrea Panontin left comment #8658 on Lemma 15.11.6 in More on Algebra

In the proof of $(3)\Rightarrow(1)$ in "suppose given a factorization $\overline{f}=g_0h_0$ with $g_0,h_0\in A/I[T]$ monic" I would add the (implicit) assumption that $(g_0,h_0)$ is the unit ideal. Then it is clear that we have a decomposition of $B/IB$ , which should be $B/IB=A/I[T]/(g_0)×A/I[T]/(h_0)$ (the text is missing the quotient by I in the second factor)

On Sep 07, 2023 Sergey Guminov left comment #8657 on Section 96.14 in Sheaves on Algebraic Stacks

There are two instances of "wich" instead of "which" in the first two lemmas on this page.

On Sep 07, 2023 Andrea Panontin left comment #8656 on Lemma 15.12.1 in More on Algebra

When showing that the colimit is a henselian pair the following "Since $A^h/I^h=A/IB$ " should instead read "Since $A^h/I^h=A/I$ ".

On Sep 06, 2023 nkym left comment #8655 on Lemma 36.22.6 in Derived Categories of Schemes

Right before "the second equality by Lemma ..." in the proof, $O_{X}$ should be $O_{S'}$ .

On Sep 06, 2023 ZL left comment #8654 on Lemma 21.37.2 in Cohomology on Sites

There seems to be typos on the superscript for the $\mathop{\mathrm{Ext}}$ -spectral sequence: " $E _ 1^{p, q} = \mathop{\mathrm{Ext}} \nolimits ^ p _ {\mathcal{O}_\mathcal {C}}( \mathcal{K} ^ {-q}, g ^ {-1}\mathcal{I}) \Rightarrow \mathop{\mathrm{Ext}} \nolimits ^ {p + q} _ {\mathcal{O} _\mathcal {C}}( \mathcal{K}^\bullet , g^{-1}\mathcal{I}) = 0.$ " should be " $E _ 1^{p, q} = \mathop{\mathrm{Ext}} \nolimits ^ q _ {\mathcal{O}_\mathcal {C}}( \mathcal{K} ^ {-p}, g ^ {-1}\mathcal{I}) \Rightarrow \mathop{\mathrm{Ext}} \nolimits ^ {p + q} _ {\mathcal{O} _\mathcal {C}}( \mathcal{K}^\bullet , g^{-1}\mathcal{I}) = 0.$ " Similarly the non-zero terms in the $E _ 1$ -page should be $E _ 1^ {q,0}=\mathop{\mathrm{Hom}}\nolimits _{\mathcal{O} _\mathcal {C}}( \mathcal{K}^{-q}, g^{-1}\mathcal{I})$ .

On Sep 04, 2023 Branislav Sobot left comment #8653 on Section 10.84 in Commutative Algebra

Should it be Q_{\alpha}=Q\cap P_{\alpha} in condition (6)?

On Sep 03, 2023 nkym left comment #8652 on Proposition 15.78.3 in More on Algebra

In the explanation of $\pi$ right after introducing the notation, $i$ should be $c$ .

On Sep 03, 2023 Yu left comment #8651 on Definition 8.2.2 in Stacks

Typo: "The subpresheaf Isom(x,y) whose values over V is the set of isomorphisms..." should be "The subpresheaf Isom(x,y) whose value over V is the set of isomorphisms...".

On Sep 01, 2023 Elías Guisado left comment #8650 on Lemma 5.4.2 in Topology

(Sorry: a finite scheme is not necessarily affine. However, schemes with 1 or 2 points always are.)

On Aug 31, 2023 Michael left comment #8649 on Section 3.7 in Set Theory

A minor point, but shouldn't there be a resource for limits and colimits in the bibliography, or an appendix of sorts? It's a bit jarring that the chapter discusses elementary set theory, but assumes colimits are already known.