The Stacks project

Comments 1401 to 1420 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 #8232 on Lemma 76.31.1 in More on Morphisms of Spaces

Thanks and fixed here.


On left comment #8231 on Section 4.10 in Categories

Going to leave this alone for now.


On left comment #8230 on Definition 10.144.1 in Commutative Algebra

Yes, because is isomorphic to .


On left comment #8229 on Lemma 36.8.2 in Derived Categories of Schemes

Thanks and fixed here.


On left comment #8228 on Section 33.36 in Varieties

Yes, but perhaps not essential to change this now. I will take a pull request for this.


On left comment #8227 on Lemma 10.134.11 in Commutative Algebra

Feel free to type up a brief explanation and submit it. Thanks!


On left comment #8226 on Definition 94.19.3 in Algebraic Stacks

Thanks and fixed here.


On left comment #8225 on Lemma 10.53.5 in Commutative Algebra

Dear Anon, OK, I agree we could do a bit better here. For example, the product decomposition at the end of the argument holds because the are orthogonal to each other and sum up to . Then we could add some lemmas that is a localization of if is an idempotent. We could add a lemma that if a is a localization and is local, then is the localization of at a prime ideal. We could add the lemma you stated in #8124. I don't want this to become a long unwieldy thing however, so maybe there is a short sweet proof of this someone could tell me?


On left comment #8224 on Section 31.23 in Divisors

Feel free to write something and submit it.


On left comment #8223 on Definition 10.6.1 in Commutative Algebra

Dear Reginald Anderson, this is indeed a common practice in mathematics. Please only comment on this when you see a case of it where you are genuinly confused.


On left comment #8222 on Lemma 29.21.7 in Morphisms of Schemes

I agree with what you wrote, but I am going to leave this as is for now.


On left comment #8221 on Lemma 10.127.15 in Commutative Algebra

Thanks and fixed here.


On left comment #8220 on Example 29.43.2 in Morphisms of Schemes

Going to leave this alone. Of course, I agree with you.


On left comment #8219 on Lemma 12.6.4 in Homological Algebra

Feel free to type something up and submit.


On left comment #8218 on Lemma 27.10.4 in Constructions of Schemes

Thanks and fixed here.


On left comment #8217 on Lemma 30.19.3 in Cohomology of Schemes

Going to leave as is.


On left comment #8216 on Lemma 12.5.8 in Homological Algebra

Thanks and fixed here.


On left comment #8215 on Lemma 58.31.3 in Fundamental Groups of Schemes

Sure. I made it a separate lemma. But I think this original one is what we always use. See this.


On left comment #8214 on Section 58.31 in Fundamental Groups of Schemes

Thanks and fixed here.


On left comment #8213 on Lemma 13.5.10 in Derived Categories

Thanks and fixed here.