Recent comments—The Stacks project

Comments 2121 to 2140 out of 9050 in reverse chronological order.

On Jun 21, 2022 Zhiyu Z left comment #7438 on Section 20.42 in Cohomology of Sheaves

@7424 Can you be more specific on where "20.39" reads "20.38"? There seems to be no "20.38" Tag used in the section..

On Jun 21, 2022 Zhiyu Z left comment #7437 on Section 7.5 in Sites and Sheaves

@7410 " colim_I F " is the notation for the colimit of a functor F: I -> C (an object in C) . See Definition 4.14.2.

On Jun 20, 2022 nkym left comment #7436 on Lemma 10.134.16 in Commutative Algebra

The result for a single choice of $\alpha$ and $\beta$ seem to yield not the result for the general case, but a similar isomorphism with more $S_g$ added than $m$ or $n$ .

On Jun 20, 2022 Anonymous left comment #7435 on Lemma 101.7.10 in Morphisms of Algebraic Stacks

Typo: In the second to last sentence of the proof, we should have $U' \times_{W} (W \times_{\mathcal{Y}} \mathcal{X})$ instead of $U' \times_{W} \times_{W} (W \times \mathcal{Y} \mathcal{X})$ .

On Jun 20, 2022 nkym left comment #7434 on Lemma 31.22.12 in Divisors

In the reduction to the case $X = \mathbb{A}_S^n$ , to show that $h\circ i$ is quasi-regular by 067Q, it looks like $i$ needs to be $H_1$ -regular, not just quasi-regular.

On Jun 20, 2022 nkym left comment #7433 on Lemma 17.31.5 in Sheaves of Modules

I found a small typo "explicity" in the proof.

On Jun 20, 2022 Zhiyu Liu left comment #7432 on Lemma 66.19.7 in Properties of Algebraic Spaces

In the third row of the proof of Lemma 04K0, "...fitting into the diagram of Definition 0486." should be "...fitting into the diagram of Definition 04JV."

On Jun 20, 2022 Zhang left comment #7431 on Theorem 59.89.2 in Étale Cohomology

First proof, 5th paragraph ("Next, ..."): "Hence it suffices to that" should be "Hence it suffices to show that".

On Jun 17, 2022 Taro konno left comment #7430 on Lemma 66.16.1 in Properties of Algebraic Spaces

In the proof of part (2), $\chi _ W$ is etale by Lemma 29.36.18 instead of Lemma 29.36.19, I think. And there is typo: "To prove part (2)" should be "To prove part (3)"

On Jun 16, 2022 Hossein Faridian left comment #7429 on Theorem 92.12.4 in The Cotangent Complex

How does one obtain the dual to Quillen's spectral sequence involving Hom and Ext? The statement is in "On the Co(homology) of Commutative Rings (Quillen)" with no proof.

On Jun 16, 2022 Elías Guisado left comment #7428 on Lemma 12.14.10 in Homological Algebra

not *before

On Jun 16, 2022 Elías Guisado left comment #7427 on Lemma 12.14.10 in Homological Algebra

I agree with @#5081: not after I did read Laurent's comments I could understand well the proof.

On Jun 15, 2022 Jianing Li left comment #7426 on Lemma 10.161.8 in Commutative Algebra

The proof seems also work when R is not normal.

On Jun 15, 2022 David Holmes left comment #7425 on Section 29.37 in Morphisms of Schemes

Hi Andrés Ibáñez Núñez,

I think I agree with your criticism of the argument. But it seems to me that Lemma 01VI implies that $f$ is separated, and Lemma 09MP implies that $Y$ is separated, and together these imply that $X$ is separated, so in fact we are OK. Does that seem reasonable?

On Jun 15, 2022 Nik left comment #7424 on Section 20.42 in Cohomology of Sheaves

Some minor typos: some of the references read 20.38.X, although they link to 20.39.X.

On Jun 14, 2022 Andrés Ibáñez Núñez left comment #7423 on Section 29.37 in Morphisms of Schemes

In the proof of 0892, when using 01PW I believe you actually need the fact that the map 0B5L is an isomorphism. Thus I believe that an argument is needed to prove that X is quasi-separated or a direct argument to prove that 0B5L is an isomorphism.

On Jun 13, 2022 Sungwoo left comment #7422 on Lemma 76.19.13 in More on Morphisms of Spaces

Is $i^*\Omega_{X/B}?$ in the lemma typo?

On Jun 13, 2022 Alex Scheffelin left comment #7421 on Section 47.7 in Dualizing Complexes

Hi, I think that the lemma is okay as is, as the hypotheses force $\mathfrak{m}_RS = \mathfrak{m}_S$ . Namely, if $R/\mathfrak{m}_R\cong S/\mathfrak{m}_RS$ , then as the former is a field, the latter is as well so $\mathfrak{m}_RS$ is maximal. I think that this could probably be noted.

On Jun 11, 2022 Laurent Moret-Bailly left comment #7420 on Lemma 33.38.5 in Varieties

Beginning of proof: I would specify that the $\mathcal{L}_{i}$ 's
are assumed globally generated.

In the second sentence, it should be "sections $t_{i,j}$ of $\mathcal{L}_i$ ".

On Jun 11, 2022 Torsten Wedhorn left comment #7419 on Lemma 15.65.5 in More on Algebra

In several places (in (2), (3), (4) and two times in the proof) it should be $D(R)$ instead of $D(A)$ . There is a (small) risk for confusion here since the index set is also denoted by $A$ .