Recent comments—The Stacks project

Comments 1681 to 1700 out of 9050 in reverse chronological order.

On Dec 20, 2022 Karl Schwede left comment #7935 on Section 15.73 in More on Algebra

It would be nice to also point out the cases where things like Lemma 0A67 and Lemma 0BYN are isomorphisms (unless this is already done elsewhere that I missed?) See for instance Foxby's "Isomorphisms between complexes with applications to the homological theory of modules".

On Dec 20, 2022 olof left comment #7934 on Lemma 4.24.2 in Categories

ok i understanded

On Dec 20, 2022 olof left comment #7933 on Lemma 4.24.2 in Categories

And,if that isomorphism is true,then proof is no need

On Dec 20, 2022 olof left comment #7932 on Lemma 4.24.2 in Categories

"For each y choose an object v(y)"Why can we 'choose' v(y) instead of 'there exists a U in category C'?The definition of representable functor says that 'exists'.

On Dec 19, 2022 quasicompact left comment #7931 on Lemma 37.2.3 in More on Morphisms

Reference: EGA I, Proposition (5.1.9)

On Dec 17, 2022 Peng Du left comment #7929 on Lemma 15.91.23 in More on Algebra

I'm wondering if being derived complete satisfies faithful flat descent: if $A\to B$ is faithful flat, $I$ a finitely generated ideal in $A$ , does the left adjoint to the restriction functor have similar property? That is, for $K\in D(A)$ , we have $K\in D_{comp}(A, I)$ iff $K\otimes_A^{\bf L}B\in D_{comp}(B, IB)$ ?

I'm mainly interested in the case when $B=\prod_{i=1}^{n}A_{f_i}$ , where the $f_i$ 's generates the unit ideal in $A$ .

(BTW, is there a way for me to be noticed if a comment is responded?)

On Dec 17, 2022 Felipe Zaldivar left comment #7927 on Section 15.68 in More on Algebra

On Definition 15.68.1, it says "We say K as projective-amplitude" , it must be: " We say K has projective-amplitude" (change "as" to "has")

On Dec 16, 2022 Laurent Moret-Bailly left comment #7925 on Section 9.12 in Fields

@7923: take $K=\mathbb{F}_2(t)$ , $P(x)= x^4+x^2+t$ .

On Dec 15, 2022 gary knott left comment #7923 on Section 9.12 in Fields

Can you give an example where the separable degree (the number of distinct roots) of an irreducible polynomial over an infinite characteristic-value p field is not relatively-prime to the inseparable (common multiplicity of the roots) degree?

On Dec 14, 2022 Peng Du left comment #7922 on Definition 10.96.2 in Commutative Algebra

I suggest to write (0) in the footnote as '0' or '{0}'.

On Dec 13, 2022 y2k left comment #7921 on Lemma 30.14.3 in Cohomology of Schemes

Shall we make the following changes: 1. $N=\bigoplus_{n\geq0}\Gamma(X,\widetilde M(n))$ , the definition of $N$ in the 2nd sentence of the proof, changes to $N=\bigoplus_{n\in\mathbb Z}\Gamma(X,\widetilde M(n))$ ; 2. $N'=\bigoplus_{n\geq0}N$ changes to $N'=\bigoplus_{n\geq0}N_n$ ; 3. $K'=\bigoplus_{n\geq0}N_n$ changes to $K'=\bigoplus_{n\geq0}K_n$ .

On Dec 13, 2022 y1k left comment #7920 on Lemma 30.14.3 in Cohomology of Schemes

There are two $\Gamma(X,\widetilde M(n)$ in the sentence containing the non-diagram equation.

On Dec 11, 2022 Peng Du left comment #7919 on Section 15.64 in More on Algebra

One line below (15.64.0.1), "A module is called pseudo-coherent of we can find such a resolution..." "of" should be "if".

On Dec 10, 2022 Peng Du left comment #7918 on Lemma 15.74.13 in More on Algebra

What is a, b relevant here?

On Dec 10, 2022 q1k left comment #7917 on Lemma 42.24.3 in Chow Homology and Chern Classes

The line bundle L is stated twice

On Dec 10, 2022 Masugi Kazuki left comment #7916 on Lemma 10.136.14 in Commutative Algebra

Sorry, I cannot understand why $R \to S$ is locally free, and $A \to A'$ is injection. (c.i.-ness of fiber is okay: because of finiteness, if $R \to S$ is locally free, it is faithfully flat and syntomic.)

On Dec 06, 2022 Svetlana Makarova left comment #7909 on Section 48.27 in Duality for Schemes

In Lemma 0FVV (2), "dimension d" is undefined, maybe write "dimension dim X"?

It is also not obvious to me that a proper scheme over a field should be finite-dimensional, because there are affine noetherian schemes over fields which are not, and I don't see a priori why they cannot be embedded into a proper scheme. Why does the lemma talk about dimension of X as if it is alway finite?

On Dec 06, 2022 qyk left comment #7908 on Lemma 42.29.9 in Chow Homology and Chern Classes

Should the final $\mathrm{CH}_{k+r}(D)$ be $\mathrm{CH}_{k+r}(D')$ ?

On Dec 06, 2022 Laurent Moret-Bailly left comment #7907 on Lemma 54.16.9 in Resolution of Surfaces

Wrong case numbering in the proof: (2) should be (1), and (3) should be (2).

On Dec 05, 2022 chris left comment #7906 on Section 3.9 in Set Theory

This page would benefit from a forward reference to what a scheme is.