The Stacks project

Comments 2201 to 2220 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 Tim Holzschuh left comment #7349 on Definition 53.3.1 in Algebraic Curves

Typo: "...where in an invertible -module ..."


On Yijin Wang left comment #7348 on Lemma 30.20.3 in Cohomology of Schemes

Maybe there is a typo in the proof of lemma 30.20.3: In paragraph four,the last but two lines,I think 'we see that B_n⋅y_i⊂Ker(M_{n+d_i}→M_n)' should be 'we see that B_n⋅y_i⊂Ker(M_{n+d'_i}→M_n)' .


On Alejandro González Nevado left comment #7347 on Lemma 7.21.5 in Sites and Sheaves

SS: Sheafification is redundant in topoi morphisms associated to simultaneously continuous and cocontinuous site functors.


On Alejandro González Nevado left comment #7346 on Lemma 7.21.2 in Sites and Sheaves

SS: Composition of site functors respects cocontinuity of site functors.


On Alejandro González Nevado left comment #7345 on Lemma 7.14.4 in Sites and Sheaves

SS: Composition of site functors respects continuity of site functors.


On Alejandro González Nevado left comment #7344 on Lemma 7.10.13 in Sites and Sheaves

Slogan suggestion (from a sentence used in the proof of Lemma 00XK): Colimit in category of sheaves equals sheafification of colimit in category of presheaves.


On Laurent Moret-Bailly left comment #7343 on Lemma 72.9.1 in Algebraic Spaces over Fields

I think you get a non-cohomological proof by using the stratification result Tag 07ST, the case of schemes (Tag 0CKV), and an obvious induction.


On Alejandro González Nevado left comment #7342 on Lemma 7.17.8 in Sites and Sheaves

Same TeX typo in the last coproduct of the proof (last paragraph) and in the sentence "this is done shown".


On Alejandro González Nevado left comment #7341 on Lemma 7.17.8 in Sites and Sheaves

TeX typo in subindex of first coproduct in the proof (3rd paragraph).


On Alejandro González Nevado left comment #7340 on Lemma 7.17.6 in Sites and Sheaves

Slogan suggestion: finite copoducts of sheaves conserve quasi-compactness.


On Alejandro González Nevado left comment #7339 on Lemma 7.17.5 in Sites and Sheaves

Slogan suggestion: sheaf surjections transmit quasi-compactness.


On left comment #7338 on Lemma 10.107.3 in Commutative Algebra

This is not true because in particular taking would give that and there are nontrivial epimorphisms of rings, for example .


On JS left comment #7337 on Lemma 10.107.3 in Commutative Algebra

Unless I'm mistaken, this can be strengthened: if is an epimorphism of rings and is any ring map, then is an isomorphism. Proof: Use either the fact that if and are -modules and is a ring epimorphism, then the natural map is an isomorphism, or write


On left comment #7336 on Section 82.9 in Chow Groups of Spaces

Thanks and fixed here.


On left comment #7335 on Section 9.13 in Fields

OK! Well, then I am going to leave it...


On left comment #7334 on Theorem 59.61.1 in Étale Cohomology

Thanks and fixed here.


On left comment #7333 on Lemma 30.20.9 in Cohomology of Schemes

Yes, stating both would probably be optimal, but I will leave that for another day. Thanks for the comments!


On left comment #7332 on Lemma 76.40.2 in More on Morphisms of Spaces

I've run out of steam for today, so I am going to leave this as is.


On left comment #7331 on Lemma 36.37.1 in Derived Categories of Schemes

Thanks and fixed here.


On left comment #7330 on Lemma 29.34.17 in Morphisms of Schemes

Going to leave this as is for now. But yes what you say is true.