The Stacks project

Comments 1 to 20 out of 4100 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 #4351 on Lemma 13.15.12 in Derived Categories

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On left comment #4350 on Situation 13.15.1 in Derived Categories

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On awllower left comment #4349 on Lemma 13.34.3 in Derived Categories

I think in the proof the composition is supposed to be ?


On left comment #4347 on Section 95.19 in Morphisms of Algebraic Stacks

Typo in the proof of Lemma 95.19.4 : In the second to last sentence it should say "Hence is an isomorphism"


On David Loeffler left comment #4346 on Lemma 13.31.8 in Derived Categories

trivial typo: "be homological functor" --> "be a homological functor"


On Manuel Hoff left comment #4345 on Definition 18.5.1 in Modules on Sites

I think there is a word missing in the second sentence: ...which is the sheafification of the free abelian presheaf on .


On Tim Holzschuh left comment #4344 on Definition 53.2.1 in Fundamental Groups of Schemes

typo: 'sometime'


On Manuel Hoff left comment #4343 on Remark 15.67.4 in More on Algebra

In the sentence "The category of super vector spaces has an internal hom which we denote .", i think "internal hom" should be replaced by something like "duals".


On Kazuki Masugi(馬杉和貴) left comment #4342 on Lemma 28.3.1 in Morphisms of Schemes

in (2), " is quasi-separated" should be " is quasi-separated".


On Manuel Hoff left comment #4341 on Section 15.57 in More on Algebra

I have a question concerning the material in this section. For a ring and a complex of -modules one defines the derived tensor product . But I can't find any reference to a relation with the functor sending . Is it true that is defined everywhere on in the sense of Section 13.15 (Tag 05S7) and that we have as endofunctors of ?


On Yairon Cid Ruiz left comment #4340 on Lemma 9.15.7 in Fields

Small typo in part (2): It should be added "any".


On David Speyer left comment #4339 on Lemma 10.119.3 in Commutative Algebra

I don't know if you have a standard convention about marking uses of Choice. If so, it might be worth pointing out that this argument requires Choice; see https://mathscinet.ams.org/mathscinet-getitem?mr=422022 . I ran across this page while trying to find out if Choice was needed for this Lemma, so maybe this comment will help the next person.


On ExcitedAlgebraicGeometer left comment #4338 on Section 10.5 in Commutative Algebra

A potential lemma of interest here: if a module is finitely presented, then any generating set has a finite presentation. The


On Manuel Hoff left comment #4337 on Lemma 13.29.8 in Derived Categories

In the formulation of the Lemma, it is mentioned two times that the complexes are K-injective (one time in the second sentence and a second time in (1)).


On Manuel Hoff left comment #4336 on Definition 4.26.1 in Categories

In LMS2, the notation doesn't make it entirely clear to me how is quantified. Maybe one wants to mention more explicitly that given and as in the diagram, there exist and as in the diagram (same applies to RMS2).


On Elden left comment #4335 on Lemma 28.44.11 in Morphisms of Schemes

I think in the statement Lemma 28.44.11 you want to say that is of finite presentation and furthermore induces a universal homeomorphism on .


On left comment #4334 on Lemma 10.14.2 in Commutative Algebra

@#4333: No, this is not intentional. This is an issue which might have been caused by the server move (although it's unclear to me how), and I made a GitHub issue at https://github.com/gerby-project/gerby-website/issues/141.

I will look into it today or tomorrow. For now you can go to the section page, where for some reason the slogan is still displayed correctly.


On comment_bot left comment #4333 on Lemma 10.14.2 in Commutative Algebra

The slogan of this tag is displayed as "None". Is this intentional?


On ExcitedAlgebraicGeometer left comment #4332 on Section 7.10 in Sites and Sheaves

Can sheafification be generalized to presheaves taking values in arbitrary categories (or at least a setting more general than presheaves of "nice" concrete categories)?


On suggestion_bot left comment #4331 on Section 5.26 in Topology

I think it would be good to insert the following basic lemma somewhere close to the beginning of this section.

Lemma. Any open subset of an extremally disconnected space is extremally disconnected.