Recent comments—The Stacks project

Comments 1 to 20 out of 3279 in reverse chronological order.

On Jun 17, 2018 Matthieu Romagny left comment #3395 on Lemma 10.46.2 in Commutative Algebra

Remove "algebraically" in the statement of the Lemma.

On Jun 17, 2018 Matthieu Romagny left comment #3394 on Section 92.14 in Properties of Algebraic Stacks

Remove "for" in statement of condition (1).

On Jun 08, 2018 Vignesh left comment #3390 on Section 10.96 in Commutative Algebra

Sorry about the typo in my comment, in the second paragraph, I wanted to say:

By Lemma 10.86.1, we get that $0\to \lim K/(I^nR^t\cap K)\to (R^t)^\wedge \to M^\wedge \to 0$ is exact. By Artin-Rees lemma, $\lim K/(I^nR^t\cap K)=K^\wedge$ . Therefore we get $0\to K^\wedge\to (R^t)^\wedge \to M^\wedge \to 0$ is exact as required.

On Jun 08, 2018 Vignesh left comment #3389 on Section 10.96 in Commutative Algebra

A different presentation of the proof of Lemma 10.96.1:

Consider a presentation of module M (which is f.g. by assumption) $0\to K\to R^t\to M\to 0$ We get that $0\to K/(I^nR^t\cap K)\to R^t/(I^nR^t)\to M/(I^nM)\to 0$ is exact. (Here $K$ is viewed as a submodule of $R^t$ .) One sees this by observing that $I^nR^t$ maps surjectively onto $I^nM$ .

By Lemma 10.86.1, we get that $0\to \lim K/(I^nR^t\cap K)\to R^\wedge \to M^\wedge \to 0$ is exact. By Artin-Rees lemma, $\lim K/(I^nR^t\cap K)=K^\wedge$ Therefore we get $0\to K^\wedge\to R^\wedge \to M^\wedge \to 0$ is exact as required.

A correction in the proof of Lemma 10.96.2:

Here I think you mean an arbitrary ideal $J$ in R (and not specifically the ideal $I$ w.r.t. which $R$ is completed): $J \otimes _ R R^\wedge \to R \otimes _ R R^\wedge = R^\wedge$ .

On Jun 01, 2018 Dario left comment #3388 on Lemma 53.2.2 in Fundamental Groups of Schemes

Typo: Let $K^{sep}$ a separable closure...missing be

On Jun 01, 2018 Dario left comment #3387 on Lemma 54.70.8 in Étale Cohomology

Typo in (1): the map on stalks should also go from F to G

On Jun 01, 2018 Dario left comment #3386 on Section 5.28 in Topology

Typo: Moreo generally... Just above 0BDS

On May 27, 2018 shanbei left comment #3385 on Section 15.8 in More on Algebra

In the third line of proof of (7) in Lemma 07ZA, perhaps you meant the rank of image is less than n instead of \leq?

On May 26, 2018 Daniel Litt left comment #3384 on Section 1.2 in Introduction

Lines (1), (2), (7), and (11) seem not to be rendering correctly on my computer.

On May 23, 2018 Reimundo Heluani left comment #3382 on Section 38.12 in Groupoid Schemes

In Lemma 38.12.2, $f$ should be $f:Y\rightarrow X$ .

On May 23, 2018 Job Rock left comment #3381 on Lemma 8.2.3 in Stacks

I suspsect we want $x,y\in\text{Ob}((\mathcal{S}_1)_U)$ in the statement of the Lemma.

On May 23, 2018 Kazuki Masugi left comment #3380 on Section 5.8 in Topology

And in the proof of the Lemma5.8.5(2), "Hence there exists $x\in Y$ with $\overline{\{x\}}=Y$ . It follows $\overline{\{x\}}\cap Y=Y$ ." should be "Hence there exists $x\in Z$ with $\overline{\{x\}}=Z$ . It follows $\overline{\{x\}}\cap Y=Z$ ."

On May 23, 2018 Kazuki Masugi left comment #3379 on Section 5.8 in Topology

In the proof of the Lemma5.8.5(1), "x,y \in X" should be "x,y \in Y"

On May 23, 2018 Kazuki Masugi left comment #3378 on Section 5.7 in Topology

In the Lemma5.7.6, "p(T)" should be "f(T)".

On May 20, 2018 Johan left comment #3377 on Lemma 9.20.7 in Fields

Actually, rather you should look here since my previous attempt was erroneous.

On May 20, 2018 Kazuki Masugi left comment #3376 on Section 4.26 in Categories

There are typos in the proof of the Lemma 4.26.10; b is equivalence class of the pair (h , t) and a is of (g , s).

On May 19, 2018 Johan left comment #3375 on Lemma 4.25.1 in Categories

Thanks and fixed here.

On May 19, 2018 Johan left comment #3374 on Section 28.32 in Morphisms of Schemes

Thanks! I've tried to fix this in this commit but as you perhaps know, the XyJax stuff is a bit shaky.

On May 19, 2018 Johan left comment #3373 on Section 36.55 in More on Morphisms

Thanks, fixed here.

On May 19, 2018 Johan left comment #3372 on Section 84.22 in The Cotangent Complex

Thanks, fixed here.