Stacks project -- Comments

#4016 on tag 02LD by Alexander Schmidt

Alexander Schmidt — Thu, 21 Feb 2019 11:52:03 GMT

Comment on [Comment #4011 by Janos Kollar on February 19, 2019 at 12:09]

Indeed, there are many names but none of them is really good. Let me make yet another proposal: "Nisnevich neighborhood".

#4015 on tag 0D49 by Fabrice Orgogozo

Fabrice Orgogozo — Thu, 21 Feb 2019 07:55:15 GMT

In the proof of the lemma 09ZL, "Moreover, if B′′/IB′′→… is an isomorphism, then B′→eB′′ is an isomorphism too", I think it should be "Moreover, if B'/IB' →… is an isomorphism …".

#4014 on tag 04PB by Matthieu Romagny

Matthieu Romagny — Thu, 21 Feb 2019 04:06:17 GMT

After (04PC) it is written "Then the pair (a′,Z′) satisfies (1), (2)" but conditions (1) and (2) do not exist. Also in Remark 04PI remove "s" from "an F2-algebras (without unit)".

#4013 on tag 0C1D by Dario Weißmann

Dario Weißmann — Wed, 20 Feb 2019 08:40:30 GMT

typo: $g_y$ should be $g_Y$

#4012 on tag 066P by jojo

jojo — Wed, 20 Feb 2019 06:23:18 GMT

Maybe instead of

"The assumption on $R$ means that every module has a finite projective resolution of length at most $d$ , in particular every module has finite tor dimension."

you should say

""The assumption on $R$ means that every module has a finite projective resolution of length at most $d$ , in particular every module has tor dimension less $\leq d$ ."

since this is what you are proving ?

#4011 on tag 02LD by Janos Kollar

Janos Kollar — Tue, 19 Feb 2019 12:09:26 GMT

Dear Johan, it might be good to mention that your “elementary étale neighborhoods” have many different names. I believe that they are called “étale neighborhoods” in (Milne’s book, p.36), “strongly étale” in (Kurke Pfister, Roczen book , p.108) and “strictly étale” is also frequent I think.

best

János

#4010 on tag 01JF by Andrei Bengus-Lasnier

Andrei Bengus-Lasnier — Sun, 17 Feb 2019 08:46:10 GMT

In the last paragraph of the proof, I don't see why we use the open immersion property to make the $V_i$ maximal. One does not need that in order to prove they agree on overlaps.

#4008 on tag 0DRE by George Georgiev

George Georgiev — Fri, 15 Feb 2019 03:39:12 GMT

Minor typo: "univesally" -> "universally" in "...univesally catenary scheme..."

Great work otherwise. I'm learning statistics and I find field theory & set theory basics quite indispensible in understanding the nitty-gritty stuff.

#4006 on tag 0EWX by Johan

Johan — Tue, 12 Feb 2019 06:01:51 GMT

Oops, yes I will fix this later. Thanks

#4005 on tag 0EWX by Zhiyu Zhang

Zhiyu Zhang — Tue, 12 Feb 2019 12:24:16 GMT

OK, It's also because of a typo that made me confused at first : the index $b-i-1$ on the right side of $\mathop{\mathrm{Hom}}\nolimits _{D(\mathcal{A})}(H^ b(K)[-b], \tau _{\leq b - 1}K[1]) = \bigoplus \nolimits _{i < b} \mathop{\mathrm{Ext}}\nolimits _\mathcal {A}^{b - i - 1}(H^ b(K), H^ i(K))$ shall be $b-i+1$ , so $b-i+1 \geq 2$ and we can use the assumption to deduce this lemma.