The Stacks project

Comments 361 to 380 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 #9362 on Section 12.29 in Homological Algebra

Thanks very much. I have simply improved the statement of the lemma with your remark. I don't know what happens if does not have enough injectives. Changes are here.


On left comment #9361 on Section 59.31 in Étale Cohomology

Thanks and fixed here.


On left comment #9360 on Lemma 15.86.1 in More on Algebra

Fixed here.


On left comment #9359 on Lemma 76.36.2 in More on Morphisms of Spaces

I agree that the fibre is finite in general. Of course, then one needs to change the proof and statement saying: for the set is finite. But in order to talk about residue fields, we need to assume has a residue field... (for example if is quasi-separated). On the other hand, I think this lemma will only be used after a base change to an affine scheme over , so I think there is no harm leaving it as it is.


On left comment #9358 on Lemma 15.121.1 in More on Algebra

Thanks to both. Fixed here.


On left comment #9357 on Lemma 75.21.1 in Derived Categories of Spaces

Thanks and fixed here.


On left comment #9356 on Section 15.8 in More on Algebra

Thanks and fixed here.


On left comment #9355 on Section 13.5 in Derived Categories

Thanks and fixed here.


On left comment #9354 on Section 60.7 in Crystalline Cohomology

Going to leave as is.


On left comment #9353 on Definition 5.8.1 in Topology

We always use the induced topology on subsets, see Section 5.6. Going to leave as is.


On left comment #9352 on Lemma 35.11.1 in Descent

THanks and fixed here.


On left comment #9351 on Lemma 91.15.1 in Deformation Theory

Absolutely! Thanks and fixed here.


On left comment #9350 on Section 111.1 in Exercises

Rings are commutative in the Stacks project. Leaving as is.


On left comment #9349 on Lemma 8.10.1 in Stacks

Thanks and fixed here.


On left comment #9348 on Lemma 8.10.6 in Stacks

Thanks and fixed here.


On nkym left comment #9347 on Lemma 12.26.3 in Homological Algebra

should be $H^ {-n}(A_{n + 1}^\bullet )


On nkym left comment #9346 on Lemma 12.26.3 in Homological Algebra

"a boundary the boundary" should be "the boundary."


On nkym left comment #9345 on Lemma 12.26.3 in Homological Algebra

should be .


On left comment #9344 on Section 39.7 in Groupoid Schemes

Hint: Think about the case of usual groups.


On left comment #9343 on Theorem 57.13.3 in Derived Categories of Varieties

Indeed. Link 36.11.8.