The Stacks project

Comments 881 to 900 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 #8829 on Definition 13.27.1 in Derived Categories

@#8785 Okay, I just realized: if has enough injectives, then the -functor is universal because it is erasable, i.e., it satisfies the hypothesis of 12.12.4: For an object , take an injection into an injective object. Then vanishes for all by 13.18.8. Dually, if has enough projectives, one can apply the analogous argument to to deduce erasibility (and thus universality).

Is the statement of this result to be found anywhere in the SP?

(Please, erase #8828, I posted it in the wrong tag.)

On Wataru left comment #8827 on Lemma 15.89.8 in More on Algebra

In the first paragraph of the proof, it would help me more if there is reference to Lemma 05EC during the reduction to a direct sum of 's.

On DIpankar Maity left comment #8826 on Section 7.19 in Sites and Sheaves

May be somewhere you can mention the following : Let be a left adjoint to (of functors of sites). Then is continuous iff is cocontinuous.

On HilbertDing left comment #8825 on Section 38.33 in More on Flatness

Lemma 38.33.6, should be "If V has a compactification V'⊂Y over S" instead of "If V has a compactification V⊂Y over S".

On Ryo Suzuki left comment #8824 on Section 10.69 in Commutative Algebra

It might be good to add this lemma:

Let be a ring and let . Set . Let be an -module. Suppose that, for any and a homogeneous polynomial of degree , if then the coefficients of is in . Then is a -quasi-regular sequence.

It is essentially proved in the proof of Lemma 00LN. It is also appear in the proof of Lemma 062I and its proof might become cleaner by using this lemma.

On Connor Bass left comment #8823 on Lemma 14.18.5 in Simplicial Methods

Another typo, which appears twice: it should be "" for one decomposition of (which appears towards the middle of the proof) instead of "" and it should be "" instead of "" for another (which appears towards the end of the proof).

On Connor Bass left comment #8822 on Lemma 14.18.5 in Simplicial Methods

There's a typo at the end of the sentence which begins as "Here is a procedure for decomposing...". It should be "with ", instead of "".

On uikmuuyiok left comment #8821 on Equation 107.5.21.1 in The Geometry of Algebraic Stacks

This fomular can't split as two lines in pdf file. Maybe need add split enviroment.

On Alexander Schmidt left comment #8820 on Section 59.89 in Étale Cohomology

Typo in line 5 of Proof of 0EYT: uninon --> union

On uikmuuyiok left comment #8818 on Remark 5.7.4 in Topology

Bibliography author should be Engelking, Ryszard not Engelking, Rysxard

On Jakob Werner left comment #8817 on Lemma 18.40.11 in Modules on Sites

The first sentence of the lemma should read Let f be a morphism.

On Hsueh-Yung Lin left comment #8816 on Section 28.7 in Properties of Schemes

Small typo: In the proof of Lemma 28.7.9, I think we should cite Lemma 28.7.4 instead of Lemma 28.7.2.

On Laurent Moret-Bailly left comment #8815 on Lemma 110.12.5 in Examples

First displayed formula in proof: should be (twice).

On Subhranil Deb left comment #8814 on Lemma 15.55.4 in More on Algebra

I believe the map should be instead of .

On amnon yekutieli left comment #8813 on Section 110.12 in Examples

trying again to cite:

Yekutieli, A. Flatness and Completion Revisited. Algebr Represent Theor 21, 717–736 (2018). https://doi.org/10.1007/s10468-017-9735-7

On amnon yekutieli left comment #8812 on Section 110.12 in Examples

In Theorem 7.2 of my paper Flatness and Completion Revisited (DOI \ref{https://doi.org/10.1007/s10468-017-9735-7} there is an example of a ring homomorphism A \to B that's not flat, but it is adically flat (i.e. completely flat), and also A \to \hat{B} is flat.

On Thomas Manopulo left comment #8811 on Section 53.2 in Algebraic Curves

I think in Lemma 0BXY it should be mentioned that the point x lies in U, no?

On Samuel Tiersma left comment #8810 on Section 111.28 in Exercises

Exercise 02EM, part (1): the linear form should be coprime to capital F, not little f.

On left comment #8809 on Lemma 10.69.5 in Commutative Algebra

Typo: in the iso after "is the quotient of", there's a missing in the denominator of the LHS.

On Chris left comment #8808 on Section 29.11 in Morphisms of Schemes

What does the notation mean? I can't find it anywhere else in the stacks project.


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