Stacks project -- Comments

#9027 on tag 09GK by João Candeias

João Candeias — Thu, 25 Apr 2024 11:16:59 GMT

I think this is still not quite correct, as a countable product of countables is not countable (already a countable product of finite sets isn't countable), so in particular if we take $F=\mathbb{Q}$ , we see that a countable product of copies of $F$ has bigger cadinality than that of $F$ (which is equal to $\aleph_0$ ). Hence this is not a valid argument.

However, we are only interested in a subset of $F^{\mathbb{N}}$ , which can be obtained as a countable union (all possible degrees $n$ ) of finite products (all possible $n+1$ coefficients of the polynomial) of $F$ , and this is indeed bounded by $\max{(\aleph_0,|F|)}$ .

#9026 on tag 0G5Z by James

James — Thu, 25 Apr 2024 02:04:22 GMT

"zero" is repeated twice in the 3rd line of the proof.

#9025 on tag 01KH by Liam

Liam — Wed, 24 Apr 2024 04:44:17 GMT

In the proof of Lemma 26.21.7 (b), it's not obvious that the collection of U $\times$ V forms an open cover, however, we can check this easily by checking that every k-point is in one of this collection for every field.

#9024 on tag 00S0 by Zheng Yang

Zheng Yang — Sat, 20 Apr 2024 06:02:19 GMT

There is a typo below Defn. 07BN in the description of the cotangent complex. The sentence should be corrected to read: "... the chain complex associated to the simplicial module..."

#9023 on tag 00NY by jack

jack — Sat, 20 Apr 2024 08:54:22 GMT

Here the formula defining R is recursive, but it should just be C^\inft(\mathbb{R}) of course. 052H has the same problem since it is a copy of this.

#9022 on tag 09DT by Zhenhua Wu

Zhenhua Wu — Fri, 19 Apr 2024 05:00:04 GMT

In the last line, the function $\sigma \circ (\sigma^\prime)^{-1}$ should be $\sigma^{-1}\circ \sigma^\prime$ .

#9021 on tag 010I by Stacks project

Stacks project — Fri, 19 Apr 2024 03:53:36 GMT

@#8412 Thanks and fixed here.

#9020 on tag 04GG by Stacks project

Stacks project — Fri, 19 Apr 2024 03:45:57 GMT

Thanks to the comments 8410, 8561, 8796, 8797. Fixed here.

#9019 on tag 00GH by Stacks project

Stacks project — Fri, 19 Apr 2024 03:30:57 GMT

Thanks and fixed here.

#9018 on tag 05TA by Stacks project

Stacks project — Fri, 19 Apr 2024 03:27:48 GMT

Thanks, this is indeed better. Fixed here.