Comments 1 to 20 out of 7686 in reverse chronological order.


On Won Seong left comment #8273 on Section 12.26 in Homological Algebra

There's a typo at the very first of this section 'cateogry'

On Zhenhua Wu left comment #8272 on Lemma 33.9.3 in Varieties

In (7), ''geometrically reduced and connected'' should be replaced by ''geometrically reduced and geometrically connected'' both in the statement and proof to reduce ambiguity.

On Wouter Rienks left comment #8271 on Lemma 50.15.7 in de Rham Cohomology

I think it should be $\mathbb{A}^{m + 1}_T = \Spec(P)$, not $\Spec(B)$.

On Xiaolong Liu left comment #8268 on Lemma 59.29.9 in Étale Cohomology

In (4) it should be $\mathcal{F}\mapsto\mathcal{F}_{\bar{s}}$ instead of $\mathcal{F}\mapsto\mathcal{F}_{\bar{x}}$.

On Haohao Liu left comment #8265 on Lemma 20.11.1 in Cohomology of Sheaves

It seems that here "covering" means an open covering.

On left comment #8264 on Proposition 10.35.19 in Commutative Algebra

See Section 10.2.

On William Sun left comment #8262 on Proposition 10.35.19 in Commutative Algebra

$\mathfrak p = \mathfrak q\cap R$ is the retraction of the prime ideal $\mathfrak q\subset S$ under the (not necessarily injective) ring map $R\to S$. It might be better to clarify the abuse of notation here.

On Haohao Liu left comment #8261 on Lemma 30.6.1 in Cohomology of Schemes

It seems to me that the proof works for every abelian sheaves $F=colim F_i$.

On Matthieu Romagny left comment #8260 on Lemma 69.15.1 in Limits of Algebraic Spaces

typo in first sentence of proof: a morphism of algebraic spaces

On Xiao left comment #8259 on Section 109.33 in Examples

What is $M_i$ in the definition of $L_{n,i}=A\otimes_{\mathbb Q}...$? (The explanation below 05WK.)

On Runlei Xiao left comment #8258 on Lemma 42.2.4 in Chow Homology and Chern Classes

In Lemma 42.2.4. the $(M, N, \varphi , \psi )$ should change to $(M,N,0,0)$ if not the following exact sequence in your proof will be not well-defined.

On Haohao Liu left comment #8257 on Lemma 36.4.5 in Derived Categories of Schemes

Before applying 08D5, we should add "We can work locally on $S$, so assume $S$ is quasi-compact."

On Nicolas Weiss left comment #8256 on Lemma 13.18.9 in Derived Categories

One of the typos pointed out above hasn't been fixed in the correction, namely that $B\rightarrow E$ is a q-iso (and not something about $B\rightarrow A$).

On Haohao Liu left comment #8255 on Definition 59.18.1 in Étale Cohomology

It seems that the existence of the fiber product $U_{i_0}\times_UU_{i_1}$ is implicitly assumed.

On s.goto left comment #8254 on Section 90.2 in Deformation Theory

I think there is a typo in the formula displayed in lemma 0GPX: \Ext_A^1(NL_{A'/A},N) should be \Ext_A^1(NL_{A/A'},N). And also, "A'_1[B_1]" in the sentence "Observe that B'1 is the pushout of J' \to $A'1[B_1]$ in the proof of lemma 08S5 seems to be a typo, it should be "A'_1[E]".

On DatPham left comment #8253 on Lemma 10.168.4 in Commutative Algebra

I think we need to enlarge $i$ once more to ensure that $b_{j,i}$ maps into $1 \otimes x_j$ in $A_i \otimes_{A_0}C_0$.

On DatPham left comment #8251 on Lemma 29.36.18 in Morphisms of Schemes

I think it may be helpful to mention also a proof using the usual graph argument (which works because we have seen that (a) the diagonal of an unramified map is an open immersion, (b) an open immersion is étale, (c) being étale is preserved under composition and base change).

On left comment #8250 on Lemma 10.63.16 in Commutative Algebra

Hint: intersection means inverse image by the ring map $R \to S^{-1}R$.

On Et left comment #8249 on Lemma 10.63.16 in Commutative Algebra

I don't think the first statement of the proof about the annhilator of m is true. It does hold however if the annhilator is a prime ideal which doesn't intersect S, which is what you need anyway.

On Et left comment #8248 on Lemma 10.53.4 in Commutative Algebra

How is nakayama's lemma applied here? It's not clear to me