Recent comments—The Stacks project

Comments 1 to 20 out of 4550 in reverse chronological order.

On Jan 24, 2020 Peng DU left comment #4893 on Lemma 42.12.2 in Chow Homology and Chern Classes

In line 3 and 7 of the proof, the term (f∘g)∗[W] should be (g∘f)∗[W].

On Jan 23, 2020 Spencer Dembner left comment #4892 on Section 9.25 in Fields

Does the sentence beginning "By linear algebra..." get used? It seems like everything used later in the proof follows from the minimal polynomial fact alone.

On Jan 23, 2020 Peng DU left comment #4891 on Section 42.33 in Chow Homology and Chern Classes

Maybe it's better to change "chern" to "Chern" everywhere (I find quite a few "chern" in titles of sections in this chapter).

On Jan 23, 2020 Rankeya left comment #4890 on Lemma 10.126.1 in Commutative Algebra

First sentence of proof should say: The category $\mathcal{I}$ is non-empty as $R \rightarrow R$ is an object of it.

On Jan 22, 2020 SDIGR left comment #4889 on Lemma 98.27.7 in Morphisms of Algebraic Stacks

Typo: "Note that $U=\coprod V_i\to U$ is..." should be "Note that $U=\coprod V_i\to V$ is..."

On Jan 22, 2020 SDIGR left comment #4888 on Lemma 98.27.7 in Morphisms of Algebraic Stacks

Typo: "Note that $U=\coprodV_i\to U$ is..." should be "Note that $U=\coprodV_i\to V$ is..."

On Jan 21, 2020 Peng DU left comment #4887 on Lemma 10.51.10 in Commutative Algebra

Need assume $M\ne 0$ .

On Jan 20, 2020 QGravity left comment #4886 on Section 53.9 in Algebraic Curves

Does the genus of the curve in $\mathbb{P}^1\times \mathbb{P}^1$ fix the equation of the curve uniquely? Could you please add references for the curves in $\mathbb{P}^1\times \mathbb{P}^1$ ?

On Jan 19, 2020 Manuel Hoff left comment #4885 on Lemma 10.40.10 in Commutative Algebra

Small typo: In the first sentence of the proof, $f \in S \otimes_k R$ .

On Jan 17, 2020 Matt Larson left comment #4884 on Lemma 50.11.4 in de Rham Cohomology

I think it should say "In this way we see that $H^{2i}_{dR}(\mathbb{P}^n/A)$ is a free $A$ -module...".

On Jan 16, 2020 Rankeya left comment #4883 on Lemma 10.136.4 in Commutative Algebra

Suggested slogan: Smoothness is preserved under base change.

On Jan 14, 2020 Olivier de Gaay Fortman left comment #4881 on Section 98.18 in Morphisms of Algebraic Stacks

There seems to be a small typo in the subscript of the union in Lemma 06FZ, where $X$ should be replaced by $\mathcal X$ .

On Jan 12, 2020 Olivier de Gaay Fortman left comment #4880 on Section 64.3 in Morphisms of Algebraic Spaces

Condition (2) in the third line of this section, 'fppf local on the base', seems to be hyperlinked to the wrong place only when I download the pdf. It works well on the website, but on the pdf the link sends me to Lemma 03MU, about universal injectiveness, whereas it should send me to Definition 02KO.

On Jan 12, 2020 Aise Johan de Jong left comment #4879 on Lemma 10.51.5 in Commutative Algebra

But $M$ is assumed to be an $S$ -module so the kernel of $R \to S$ already annihilates all of $M$ .

On Jan 12, 2020 Peng DU left comment #4878 on Lemma 10.51.5 in Commutative Algebra

In the proof, it says "And if R→S is surjective, then any R-submodule of M is automatically an S-submodule", but I think that may need to assume the kernel of R→S kills the submodule N: $ker(R\to S)\subset Ann_R(N)$ (otherwise, take $I$ bigger thant $Ann_R(N)$ and $S=R/I$ , then we can't make N an S-submodule of M).

On Jan 11, 2020 Adrian left comment #4877 on Section 95.9 in Artin's Axioms

In Definition 95.9.1, the horizontal arrows in the diagram are reversed.

On Jan 10, 2020 HAO left comment #4876 on Lemma 10.148.7 in Commutative Algebra

Sorry but I can't see why Lemma 10.121.1 is needed in the proof of Lemma 10.148.7. Where did you use $S=S'\times k(q)$ ?

On Jan 10, 2020 Olivier de Gaay Fortman left comment #4875 on Section 91.13 in Algebraic Stacks

Minor typo: in the proof of Lemma 03YS, it should say 'We may think of this as a surjective étale morphism of algebraic spaces'.

On Jan 10, 2020 Olivier de Gaay Fortman left comment #4874 on Section 8.7 in Stacks

In Lemma 036Y, statements (2) and (3), the condition should be that $\mathcal S$ and $\mathcal S'$ are stacks in groupoids/setoids over $\mathcal C$ , not over $\mathcal S$ .

On Jan 10, 2020 Olivier de Gaay Fortman left comment #4873 on Section 91.11 in Algebraic Stacks

In condition (1) there seems to be a small typo, where $\mathcal C$ should be replaced by $(Sch/S)_{fppf}$ .