Stacks project -- Comments

#7810 on tag 07LT by Raffaele Lamagna

Raffaele Lamagna — Fri, 30 Sep 2022 06:45:10 GMT

Typo: I think that in the definition of $\pi$ should be

$\pi\colon L^\bullet\to (\bigoplus_{\lambda\in\Lambda\setminus\Lambda'}R)[-c]$

#7809 on tag 0FL4 by Peng Du

Peng Du — Fri, 30 Sep 2022 05:42:40 GMT

I think in condition (1), it needs add that U=Spec(A)⊂X is an (affine) open neighbourhood of x.

#7808 on tag 0FL3 by Peng Du

Peng Du — Fri, 30 Sep 2022 05:36:49 GMT

Change "After a change of coordinates with may assume" to "After a change of coordinates we may assume".

#7807 on tag 0FL2 by Peng Du

Peng Du — Fri, 30 Sep 2022 05:32:12 GMT

Needs a period at the end of statement.

#7806 on tag 02NO by David Liu

David Liu — Thu, 29 Sep 2022 02:23:46 GMT

Lemma 29.39.8. : The last line : $S \rightarrow ...$ , should it be $X \rightarrow ...$ ?

#7805 on tag 039A by Johan

Johan — Wed, 28 Sep 2022 07:46:22 GMT

Because French is better? No, it's just that I love saying that phrase. Is that OK? Please feel free to complain!

#7804 on tag 01RI by Johan

Johan — Wed, 28 Sep 2022 07:44:22 GMT

I guess my pedantic reply would be: what is a schematically dense subset? Anyway, if I read it as just a "dense subset" then the inclusion of the generic point of a variety would not be a dominant morphism (in general). So I think that would be very different for morphisms of general schemes. For a morphism between varieties, it would give the same notion.

#7803 on tag 0BGS by Johan

Johan — Wed, 28 Sep 2022 07:37:49 GMT

You use Remark 65.7.6 which in tern uses the preceding Definition 65.7.5 to define what this means. So it makes sense even if the local ring does not make sense. OK?

#7802 on tag 0D7Z by Nicolás

Nicolás — Wed, 28 Sep 2022 07:11:37 GMT

It seems that (2) is missing an explicit mention of the inductive construction, as it is not specified which morphism $Y_0 \to X_0$ are we working with. Something like "If $n=1$ , then it is a choice of a Postnikov system for $X_0$ and a choice of a distinguished [...]." (And probably, in that case (2) and (3) could be unified.)

#7801 on tag 0BGS by 羽山籍真

羽山籍真 — Wed, 28 Sep 2022 10:10:47 GMT

I would like to ask where the notion "local rings" is defined for general algebraic space, since (2) used this (maybe it would be nice if we recall it here). I only know that for decent algebraic space we have Henselian local rings and for geometric points on general algebraic space we have strict Henselian local rings...