Stacks project -- Comments

#6057 on tag 01KH by Alex Gomez

Alex Gomez — Mon, 19 Apr 2021 04:33:15 GMT

On the last sentence of the first paragraph of lemma 01KP should be $A\otimes_RB\to(A\otimes_RB)/J$ .

#6056 on tag 0GDX by Rachel Webb

Rachel Webb — Sat, 17 Apr 2021 03:05:13 GMT

In the lemma statement, $Y \rightarrow S$ should be $Y \rightarrow T$ .

#6055 on tag 0BSE by Chern

Chern — Sat, 17 Apr 2021 12:36:52 GMT

Typo: "for every for every"

#6054 on tag 031G by Jonas Ehrhard

Jonas Ehrhard — Fri, 16 Apr 2021 05:52:01 GMT

I think this lemma should be stated after the discussion of diagram 10.131.5.1 / 00RQ, since the diagram explains the colimit $\text{colim}_i \Omega_{S_i / R_i}$ .

Also, I just spend half an hour searching for the existence of colimits of rings, until I found exercise 109.2.2 / 078J. Maybe this could be referenced?

#6053 on tag 00RM by Jonas Ehrhard

Jonas Ehrhard — Fri, 16 Apr 2021 03:15:04 GMT

This might be nitpicking, but shouldn't it be $\text{d} \varphi(r) = 0$ just in front of definition 10.131.2?

#6052 on tag 0FKR by Hans Schoutens

Hans Schoutens — Thu, 15 Apr 2021 05:42:25 GMT

In 2nd line of the statement of Lemma 0FKT, ...where F^\bullet be a bounded... should be ...where G^\bullet is a bounded...

#6051 on tag 0EBQ by Ashwin Iyengar

Ashwin Iyengar — Wed, 14 Apr 2021 09:59:00 GMT

Should the first equation read $U = \mathrm{Spec}(A) \backslash \left( V(\mathfrak p_1) \cup \cdots \cup V(\mathfrak p_r)\right)$ ?

#6050 on tag 03C3 by Johan

Johan — Sun, 11 Apr 2021 07:06:57 GMT

What is meant is that there is an isomorphism of fields $\varphi : K \to k'$ which induces the indentity on $k$ . More precisely, if $i : k \to K$ and $j : k \to k'$ are the inclusion maps, then $\varphi \circ i = j$ . I will improve the text the next time I go through all the comments.

#6049 on tag 0328 by Mark

Mark — Sun, 11 Apr 2021 09:35:39 GMT

It might be better to add a citation for the sentence "Then clearly $R$ is a discrete valuation ring." I think it's regular+dimension 1 (Tag 00PD (3)). (At least this was not clear to me at first glance, I wondered quite a while around noetherianness.)

#6048 on tag 03C3 by Mark

Mark — Sun, 11 Apr 2021 08:00:24 GMT

In the statement of the lemma: what does it mean for a field extension $k\subset k'$ to be isomorphic to another field extension $k\subset K$ ?