The Stacks project

Comments 561 to 580 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 #9159 on Lemma 29.32.16 in Morphisms of Schemes

Going to leave as is unless others chime in.


On left comment #9158 on Lemma 29.32.15 in Morphisms of Schemes

Going to leave as is. There is obviously also some kind of version of this for just ringed spaces under suitable hypotheses.


On left comment #9157 on Lemma 29.32.9 in Morphisms of Schemes

To save time. OK, I added this as you suggested. Thanks! See here. Of course, it would be better to prove this not using stalks and then add it to the chapter on modules on sites....


On left comment #9156 on Lemma 36.5.3 in Derived Categories of Schemes

Yes, but we can't have forward references.


On left comment #9155 on Lemma 10.155.1 in Commutative Algebra

Fixed here.


On left comment #9154 on Lemma 53.15.4 in Algebraic Curves

Thanks and fixed here.


On DatPham left comment #9153 on Lemma 37.53.1 in More on Morphisms

In the last sentence of the proof, I think you mean the nilradical, rather than the Jacobson radical.


On left comment #9152 on Theorem 7.10.10 in Sites and Sheaves

Too long


On left comment #9151 on Lemma 7.10.8 in Sites and Sheaves

Too long


On left comment #9150 on Remark 7.10.7 in Sites and Sheaves

No slogans for remarks.


On left comment #9149 on Lemma 7.10.6 in Sites and Sheaves

Too long


On left comment #9148 on Lemma 7.10.4 in Sites and Sheaves

Not pithy enough


On left comment #9147 on Lemma 7.10.3 in Sites and Sheaves

Too long


On left comment #9146 on Lemma 7.10.1 in Sites and Sheaves

OK, I have added this slogan.


On left comment #9145 on Lemma 96.10.1 in Sheaves on Algebraic Stacks

Thanks for the type; it is fixed here. The answer to your final question is yes (it's also true in the corresponding schemes case as you can more easily verify by tracing through the definitions).


On left comment #9144 on Lemma 17.28.11 in Sheaves of Modules

Yes, I think this is fine except I would use perhaps "pseudo-torsor" in stead of "torsor". You can also sheafify (so look at the sheaf of local sections), etc. Going to leave as is for now.


On left comment #9143 on Lemma 17.28.7 in Sheaves of Modules

Going to leave as is for now.


On left comment #9142 on Lemma 17.28.6 in Sheaves of Modules

Going to leave as is.


On left comment #9141 on Lemma 17.28.2 in Sheaves of Modules

Yes. Going to leave as is.


On left comment #9140 on Lemma 10.131.10 in Commutative Algebra

Going to leave as is.