The Stacks project

Comments 1421 to 1440 out of 9050 in reverse chronological order.

\begin{equation*} \DeclareMathOperator\Coim{Coim} \DeclareMathOperator\Coker{Coker} \DeclareMathOperator\Ext{Ext} \DeclareMathOperator\Hom{Hom} \DeclareMathOperator\Im{Im} \DeclareMathOperator\Ker{Ker} \DeclareMathOperator\Mor{Mor} \DeclareMathOperator\Ob{Ob} \DeclareMathOperator\Sh{Sh} \DeclareMathOperator\SheafExt{\mathcal{E}\mathit{xt}} \DeclareMathOperator\SheafHom{\mathcal{H}\mathit{om}} \DeclareMathOperator\Spec{Spec} \newcommand\colim{\mathop{\mathrm{colim}}\nolimits} \newcommand\lim{\mathop{\mathrm{lim}}\nolimits} \newcommand\Qcoh{\mathit{Qcoh}} \newcommand\Sch{\mathit{Sch}} \newcommand\QCohstack{\mathcal{QC}\!\mathit{oh}} \newcommand\Cohstack{\mathcal{C}\!\mathit{oh}} \newcommand\Spacesstack{\mathcal{S}\!\mathit{paces}} \newcommand\Quotfunctor{\mathrm{Quot}} \newcommand\Hilbfunctor{\mathrm{Hilb}} \newcommand\Curvesstack{\mathcal{C}\!\mathit{urves}} \newcommand\Polarizedstack{\mathcal{P}\!\mathit{olarized}} \newcommand\Complexesstack{\mathcal{C}\!\mathit{omplexes}} \newcommand\Pic{\mathop{\mathrm{Pic}}\nolimits} \newcommand\Picardstack{\mathcal{P}\!\mathit{ic}} \newcommand\Picardfunctor{\mathrm{Pic}} \newcommand\Deformationcategory{\mathcal{D}\!\mathit{ef}} \end{equation*}

On left comment #8212 on Remark 42.32.8 in Chow Homology and Chern Classes

Thanks and fixed here.


On left comment #8211 on Lemma 101.38.2 in Morphisms of Algebraic Stacks

Thanks and fixed here.


On left comment #8210 on Lemma 10.39.15 in Commutative Algebra

Dear teovw, i like the current argument too much but of course what you say is in some sense better... Dear Laurent, thanks. Change is here.


On left comment #8209 on Lemma 10.165.4 in Commutative Algebra

Thanks for these comments. I have made your suggested changes, see this commit.


On left comment #8208 on Section 7.50 in Sites and Sheaves

Thanks and fixed here.


On Andrea Panontin left comment #8207 on Lemma 15.11.2 in More on Algebra

I think it should be "Then . Since is locally nilpotent..." (i.e. change to in both occurences).


On left comment #8206 on Lemma 10.90.3 in Commutative Algebra

No, you have to prove this for any finite set of elements of the cokernel to prove that it is coherent. So I think it is OK.


On left comment #8205 on Lemma 37.26.6 in More on Morphisms

@#8088 OK, I added this fun curiosity in a later chapter. See this commit.


On left comment #8204 on Lemma 38.19.6 in More on Flatness

OK, I used Lemma 15.24.2 to show is finitely generated. (This of course just means that content ideals in valuation rings are always principal. So maybe this shouldn't be mentioned in this lemma. Oh well.) Thanks for the comment! See this change.


On left comment #8203 on Lemma 10.89.6 in Commutative Algebra

OK, I added this here.


On left comment #8202 on Section 26.12 in Schemes

Noted.


On left comment #8201 on Lemma 37.26.6 in More on Morphisms

@#8076 Thanks and fixed here.


On left comment #8200 on Section 61.28 in Pro-étale Cohomology

Thanks and fixed here.


On left comment #8199 on Lemma 19.12.1 in Injectives

OK, I instead replaced by in a few places. Thanks. Fixed here.


On left comment #8198 on Lemma 58.3.1 in Fundamental Groups of Schemes

Thanks and fixed here.


On left comment #8197 on Lemma 20.8.1 in Cohomology of Sheaves

Changed the slogan. See this commit.


On left comment #8196 on Lemma 55.13.3 in Semistable Reduction

Thanks and fixed here.


On Ryo Suzuki left comment #8195 on Lemma 10.135.2 in Commutative Algebra

I don't understand why equidimensionality of directly implies , although I could understand the result is true thanks to Comment #2913.


On Sándor left comment #8194 on Section 12.15 in Homological Algebra

OK, this does produce the essentially equivalent distinguished triangle, but with the other convention you get an actual ses. I know, you might say we get it with . True, but a bit ugly and it forces the reader to figure out what is. But it's your decision, so I am not arguing... :) As far as superscripts are concerned, I would prefer subscripts. Also, just for fun: Have you noticed that Hartshorne uses for the canonical truncation and for the "stupid" one in R&D? (I'm OK with it this way).


On left comment #8193 on Lemma 3.12.1 in Set Theory

It is a subcategory which is also an abelian category.