Recent comments—The Stacks project

Comments 1781 to 1800 out of 9050 in reverse chronological order.

On Sep 28, 2022 Jonas Ehrhard left comment #7800 on Lemma 33.39.5 in Varieties

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

On Sep 27, 2022 Xiaolong Liu left comment #7799 on Lemma 10.128.1 in Commutative Algebra

One should repalce ' $x\in\mathfrak{m},x\notin\mathfrak{m}^2$ ' by ' $x\in\mathfrak{m}_R,x\notin\mathfrak{m}_R^2$ '.

On Sep 27, 2022 Anonymous left comment #7798 on Lemma 13.9.5 in Derived Categories

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

On Sep 27, 2022 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 Sep 26, 2022 Laurent Moret-Bailly left comment #7792 on Proposition 99.8.4 in Quot and Hilbert Spaces

In the proof, the "coherent sheaf $\mathcal{Q}$ " is only quasi-coherent of finite presentation.

On Sep 26, 2022 Heiko Braun left comment #7791 on Lemma 13.30.1 in Derived Categories

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

On Sep 26, 2022 Jakob Werner left comment #7790 on Lemma 20.11.4 in Cohomology of Sheaves

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

On Sep 26, 2022 Pieter Belmans left comment #7789 on Equation 10.118.3.2 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 Sep 26, 2022 Joachim Jelisiejew left comment #7788 on Equation 10.118.3.2 in Commutative Algebra

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

On Sep 24, 2022 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?

On Sep 23, 2022 Laurent Moret-Bailly left comment #7786 on Definition 68.11.5 in Decent Algebraic Spaces

The problem with this phrasing is that $\kappa(x)$ does not make sense unless $x$ is a "good" point. In fact, it suffices to assume that $x$ is represented by a monomorphism; then the rest of the section remains valid.

On Sep 23, 2022 Mingchen left comment #7785 on Section 37.16 in More on Morphisms

Is there a specific reason for keeping the title of this section in french?

On Sep 23, 2022 Juhani left comment #7784 on Lemma 10.160.6 in Commutative Algebra

The original version (as far as I know) of Lemma 03C3 [EGA, ( $\mathbf{0}_{III}$ .10.3.1)] applies only to Noetherian base rings but shows that the extension is then also Noetherian. (That the Noether property is preserved in (the full version of) 03C3 is also embedded in [Bourbaki, Algèbre Commutative, Ch. X, Appendice].)

This gives immediately that R in the proof is a DVR (using also Lemma 031E). But of course the preservation of Noetherian property needs to go somewhere (in EGA it also goes via completion).

On Sep 23, 2022 Zhenhua Wu left comment #7783 on Lemma 10.114.1 in Commutative Algebra

This result got me to think that $\mathop{\mathrm{ht}}P$ , the height of a prime ideal $P$ of $k[x_1,...,x_n]$ , might be the same as $\mu(P)$ , the number of minimal generators of $P$ . A counter example is described in this link https://math.stackexchange.com/questions/96691/height-and-minimal-number-of-generators-of-an-ideal. In short, $P:=(xz−y^2,x^3−yz,z^2−x^2y)⊂\mathbb{C}[x,y,z]$ is a prime ideal with $\mathop{\mathrm{ht}}P=2$ and $\mu(P)=3$ . I suggest that we add this example after this tag.

On Sep 22, 2022 Laurent Moret-Bailly left comment #7782 on Lemma 81.3.2 in Pushouts of Algebraic Spaces

I think condition (2) can be weakened: one only needs that for all $a,b\in A$ the family $(X_i\times_X U_a \times_X U_b \to U_a \times_X U_b)_{i\in\mathcal{I}}$ is epimorphic in the category of algebraic spaces.

On Sep 22, 2022 Juhani left comment #7781 on Definition 15.36.1 in More on Algebra

The reference should point to Chaper 0 of EGA - now they point at rational functions (1st ed) or constructible sets (2nd ed). Hence: [Sections 0.7.1 and 0.7.2, EGA1]

On Sep 21, 2022 Laurent Moret-Bailly left comment #7780 on Section 81.11 in Pushouts of Algebraic Spaces

First line of section: it should be $Spaces(Y\to X,Z)$ , not $X\to Y$ .

On Sep 20, 2022 Reimundo Heluani left comment #7779 on Section 59.12 in Étale Cohomology

Hi, I think the map $G \times_{G/H} G \rightarrow G \times H$ can be given by $(g_1, g_2) \mapsto (g_1, g_1^{-1}g_2)$ or $(g_1, g_2) \mapsto (g_1, g_2^{-1} g_1)$

On Sep 19, 2022 Mingchen left comment #7778 on Lemma 15.114.4 in More on Algebra

The last sentence of the statement of the lemma needs to be better formulated.

On Sep 19, 2022 Mingchen left comment #7777 on Remark 15.114.1 in More on Algebra

(6) p-power power should be p-power