The Stacks project

Comments 701 to 720 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 #9012 on Lemma 13.16.3 in Derived Categories

Thanks! I fixed it in a slightly different way because it suffered from the same pitfall as the previous lemma. See changes.


On left comment #9011 on Lemma 13.16.1 in Derived Categories

Very good. Yes, I think this was an incomplete arguement. For example, if you look at the essentially constant system given following Definition 4.22.2, then the system lives in a subcategory (namely free -modules of even rank) but the value does not! Fixed here.


On James left comment #9010 on Section 105.7 in Introducing Algebraic Stacks

Sorry, I got too excited and posted some nonsense. The compactification is proper, not itself. Please ignore my earlier remark.


On James left comment #9009 on Section 105.7 in Introducing Algebraic Stacks

In light of the presentation of as a quotient stack (see the discussion in 072S) one can deduce i.e. it is a curve.

Also, it would be nice to mention properness which in this case is the semistable reduction theorem for elliptic curves.


On left comment #9008 on Lemma 80.3.11 in Bootstrap

Thanks and fixed here.


On left comment #9007 on Lemma 13.15.6 in Derived Categories

Thanks. I moved the discussion of the existence of to a footnote. See here.


On left comment #9006 on Lemma 13.15.4 in Derived Categories

Thanks and fixed here.


On left comment #9005 on Lemma 13.15.2 in Derived Categories

Well, personally, I would have used Lemma 4.22.11 (and its dual) if I was pressed to explain more. Let's see if we get other comments on this.


On left comment #9004 on Section 4.22 in Categories

I think this is addressed by the improvement here but let's wait till this gets pushed to the website before suggesting more changes.


On left comment #9003 on Lemma 69.22.7 in Cohomology of Algebraic Spaces

Thanks and fixed here.


On left comment #9002 on Lemma 33.39.6 in Varieties

Thanks and fixed here.


On left comment #9001 on Section 59.9 in Étale Cohomology

Thanks! Quite confusing indeed. I fixed it here.


On left comment #9000 on Lemma 31.11.6 in Divisors

Thanks and fixed here.


On left comment #8999 on Section 15.28 in More on Algebra

OK, I am not going to change the convention of shifting for chain complexes. However, for cochain complexes what you say is the convention we use. Almost all of the complexes in the Stacks project are cochain complexes.


On left comment #8998 on Proposition 13.14.8 in Derived Categories

Thanks and fixed here.


On left comment #8997 on Lemma 30.12.2 in Cohomology of Schemes

Thanks and fixed here.


On left comment #8996 on Lemma 15.88.7 in More on Algebra

@#8384: Thanks and fixed here.

@#8637: I like the proof as it stands now.


On left comment #8995 on Proposition 10.63.6 in Commutative Algebra

We already know that (1) and (3) are equal. So all that the argument does is to show that the prime is an associated prime and then we of course get that it is minimal as an associated prime. So, I think it is fine as written.


On left comment #8994 on Lemma 10.63.2 in Commutative Algebra

Going to leave as is.


On left comment #8993 on Lemma 13.5.10 in Derived Categories

Thanks and fixed here.