Recent comments—The Stacks project

Comments 1 to 20 out of 10368 in reverse chronological order.

On Apr 14, 2026 stacks project left comment #11342 on Lemma 10.119.7 in Commutative Algebra

Piotr Achinger send an example: If $K/k$ is a nontrivial extension of fields with $k$ algebraically closed in $K$ , then the ring $R =\{f \in K[[x]] : f(0) \in k\}$ is a local normal domain of dimension $1$ but not a valuation ring.

On Apr 14, 2026 nkym left comment #11341 on Lemma 15.39.1 in More on Algebra

$\mathfrak{m}$ has not been defined in the statement.

On Apr 14, 2026 nkym left comment #11340 on Lemma 15.37.5 in More on Algebra

"along the right column of the diagram above" should be "along the bottom row of the diagram above"

On Apr 14, 2026 Johan left comment #11339 on Lemma 10.50.4 in Commutative Algebra

That's because $A$ is maximal in $K$ for the relation of domination.

On Apr 14, 2026 nkym left comment #11338 on Lemma 15.37.5 in More on Algebra

"for some $n$ " in the first sentence of the proof should be "for some $t$ "

On Apr 14, 2026 Mark left comment #11337 on Section 4.13 in Categories

There is a Typo in the proof of Lemma 08LR. It starts with "Let suppose" instead of for exampl "Let us suppose"

On Apr 13, 2026 Categorical left comment #11336 on Example 27.21.2 in Constructions of Schemes

Sorry the undefined control sequence is the map $X \to P(V)$

On Apr 13, 2026 Categorical left comment #11335 on Example 27.21.2 in Constructions of Schemes

This is a minor comment. But to make your description of the displayed map $X\into P(V)$ also comes from a surjection $p^*V\to L$ for some globally generated line bundle on $L$ on $X$ . Here $p:X\to Spec(k)$ is the structure morphism. In otherwords your example can be made more canonical.

On Apr 13, 2026 nkym left comment #11334 on Lemma 15.46.3 in More on Algebra

" $v' = (x_1',\dots, x_n')\in V\cap K_\alpha$ " should be " $v' = (x_1',\dots, x_n')\in V\cap K_\alpha^n$ "

On Apr 13, 2026 nkym left comment #11333 on Lemma 15.46.5 in More on Algebra

The statement says "subfield subfield"

On Apr 13, 2026 Zhuoran Wang left comment #11332 on Lemma 43.13.2 in Intersection Theory

The second line should be "If $Z\subset Y$ is a subvariety of dimension $d$ ...".

On Apr 11, 2026 乳法专家 left comment #11328 on Lemma 59.33.1 in Étale Cohomology

The notation S_{étale} in the statement of the Lemma appears a little strange. The initial é and tale are in different formats

On Apr 10, 2026 Noah Olander left comment #11327 on Lemma 30.20.1 in Cohomology of Schemes

I think the equality $\oplus I^n\mathcal{O}_X = f^*\tilde{B}$ is not quite right as e.g. $f$ is not assumed flat, right? Of course $\oplus I^n\mathcal{O}_X$ is a quotient of $f^*\tilde{B}$ though.

On Apr 10, 2026 nkym left comment #11326 on Lemma 10.166.1 in Commutative Algebra

It seems to me that the proof only uses 04KM instead of 030R

On Apr 10, 2026 Constantin Meili left comment #11325 on Section 12.22 in Homological Algebra

I would tend to agree with Elías, because while we can take (1), (2), (3) to be the definition of the spectral sequence associated to $(A,d,\alpha)$ , it seems relevant to know that it is the same spectral sequence as the one associated to the exact couple $(H(A,d),\ H(A/\alpha A, d), \bar{\alpha},f,g)$ , which a priori isn't obvious from the definition.

On Apr 10, 2026 乳法专家 left comment #11323 on Section 59.26 in Étale Cohomology

Two lines below the second displayed formula after Definition 59.26.3, you probably mean e_1,...,e_b>1

On Apr 09, 2026 Zhuoran Wang left comment #11321 on Lemma 103.13.5 in Cohomology of Algebraic Stacks

In "(1) Since $\mathcal{X}$ is quasi-compact, there exists a surjetive and smooth morphism $\cdots$ ", "surjetive" should be "surjective".

On Apr 09, 2026 Zhuoran Wang left comment #11320 on Lemma 103.13.1 in Cohomology of Algebraic Stacks

In "(1) Since $\mathcal{X}$ is quasi-compact, there exists a surjetive and smooth morphism $\cdots$ ", "surjetive" should be "surjective".

On Apr 07, 2026 Zhuoran Wang left comment #11319 on Lemma 42.24.2 in Chow Homology and Chern Classes

The $\mathcal{O}_{X,x}$ in the last line of the proof should be $\mathcal{O}_{X,\xi}$ .

On Apr 07, 2026 Johan left comment #11318 on Lemma 15.113.5 in More on Algebra

Noah Olander pointed out a mistake with this lemma. The correct definition of P is $P = \\{\sigma \in D : (\sigma - \text{id})(\mathfrak m^i) \subset \mathfrak m^{i + 1} \ \forall i \geq 0\\}$ or $P = \\{\sigma \in D : (\sigma - \text{id})(B) \subset \mathfrak m\hbox{ and } (\sigma - \text{id})(\mathfrak m) \subset \mathfrak m^2\\}$ Only when $\kappa(\mathfrak m)$ is separable over the residue field of $A$ do we get the description of $P$ given in part (1) of the statement of the lemma. I will fix this (and the proof) the next time I go through all the comments.