The Stacks project

Comments 441 to 460 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 #9281 on Lemma 58.5.5 in Fundamental Groups of Schemes

Because \'etale morphisms are locally of finite presentation by definition and then one uses Lemma 29.48.2.


On left comment #9280 on Lemma 10.66.13 in Commutative Algebra

I instead changed n into t. Thanks and fixed here.


On left comment #9279 on Lemma 10.69.5 in Commutative Algebra

Thanks and fixed here.


On left comment #9278 on Section 111.28 in Exercises

Thanks and fixed here.


On left comment #9277 on Section 53.2 in Algebraic Curves

No.


On left comment #9276 on Section 110.12 in Examples

Thanks for these comments. Going to leave as is.


On left comment #9275 on Lemma 15.55.4 in More on Algebra

Thanks and fixed here.


On left comment #9274 on Lemma 110.12.5 in Examples

Thanks and fixed here.


On left comment #9273 on Section 28.7 in Properties of Schemes

Thanks and fixed here.


On left comment #9272 on Lemma 18.40.11 in Modules on Sites

Thanks and fixed here.


On AprilGrimoire left comment #9271 on Section 42.44 in Chow Homology and Chern Classes

I'm kind of confused by the setup here. In the setup we have is a dim function on , then what does mean? Can I understand it as the usual dimension notion?


On left comment #9270 on Remark 5.7.4 in Topology

Thanks. Fixed here.


On left comment #9269 on Equation 107.5.21.1 in The Geometry of Algebraic Stacks

Going to leave as is.


On left comment #9268 on Lemma 14.18.5 in Simplicial Methods

Thanks and fixed here.


On S.Nivodsky left comment #9267 on Section 7.32 in Sites and Sheaves

-> Life_is_hard : If the site is O_X the category of open subsets of a topological space X and inclusions between them, then for all x\in X, u : O_X -> Sets such that u(U) = empty set (if x\notin U) or {1} (if x\in U), defines a functor such that the stalk (resp. skyscraper) functor is the usual stalk (resp. skyscraper) at x. I don't have an example nor a reference, but I think there exists sites without points.


On left comment #9266 on Section 10.69 in Commutative Algebra

This is essentially just the definition of a quasi-regular sequence and I think we're just using this directly in the places you mention. Going to leave as is for now.


On left comment #9265 on Section 38.33 in More on Flatness

Do not understand. It looks fine.


On left comment #9264 on Section 7.19 in Sites and Sheaves

Thanks very much for this comment. With definitions as in the Stacks project, this "iff" is not true. When we say that a functor between sites is (co)continuous we are referring to the notions defined in Definitions 7.13.1 and 7.20.1; we do not apply our definitions to categories which do not have the structure of a site. Still, I decided to answer your question: in one direction the result is true, but in the other direction it is not. You can read this in these changes. Hopefully this will soon be online too (in this section).


On Chongyu Wang left comment #9263 on Definition 78.19.3 in Groupoids in Algebraic Spaces

There is a typo in definition 78.19.3, resp. quotient representable by an algebraic space in the penultimate line there should be a right bracket.


On andy left comment #9262 on Lemma 47.27.2 in Dualizing Complexes

sorry ignore the above comment