The Stacks project

Comments 1621 to 1640 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 Fabio Bernasconi left comment #7999 on Lemma 55.13.3 in Semistable Reduction

'Using the map Lemma 0CAB we get a map Pic(C)[h]→Pic(T)[h]' Should it refer to tag/0CAC where you construct the map Pic(C) \to Pic(T)?


On left comment #7998 on Proposition 42.57.1 in Chow Homology and Chern Classes

WhyAffineDiagonal indeed. We upgraded our treatment of chern classes of complexes to but then we missed the slight improvement one gets here. Thanks! Unfortunately, in the only spot where we use the result (so far) we do need the affineness hypothesis I think (Lemma 42.58.1). See this commit.


On WhyAffineDiagonal left comment #7997 on Proposition 42.57.1 in Chow Homology and Chern Classes

In the proof, the condition that is affine diagonal is not used. Is it redundant?


On left comment #7996 on Definition 101.8.1 in Morphisms of Algebraic Stacks

Not sure what you're asking.


On left comment #7995 on Section 35.25 in Descent

OK, I just added a reference to this for cat of schemes, see this commmit.


On left comment #7994 on Section 35.25 in Descent

Monomorphism iff diagonal isomorphism holds in any category with fibre products. OK?


On left comment #7993 on Lemma 96.18.1 in Sheaves on Algebraic Stacks

Thanks and fixed here.


On left comment #7992 on Lemma 68.4.5 in Decent Algebraic Spaces

Thanks and fixed here.


On left comment #7991 on Lemma 66.26.1 in Properties of Algebraic Spaces

Thanks and fixed here.


On left comment #7990 on Lemma 66.24.4 in Properties of Algebraic Spaces

Thanks and fixed here.


On left comment #7989 on Section 11.8 in Brauer groups

Thanks and fixed here.


On left comment #7988 on Section 3.8 in Set Theory

Both your comments are good. However, since we never use this theorem, I think the discussion as is, although somewhat imprecise, is good enough.


On left comment #7987 on Lemma 84.4.3 in More on Cohomology of Spaces

Thanks and fixed here.


On left comment #7986 on Section 15.4 in More on Algebra

Yes, it is ambiguous but I think it is OK here. Hopefully the reader understands we have a given pair in mind.


On left comment #7985 on Lemma 98.8.1 in Artin's Axioms

Thanks and fixed here.


On left comment #7984 on Section 10.153 in Commutative Algebra

Appreciate how your formulated this. Thanks! Fixed in this commit.


On left comment #7983 on Lemma 90.13.4 in Formal Deformation Theory

Thanks for these. Fixed here.


On left comment #7982 on Lemma 90.4.7 in Formal Deformation Theory

Thanks and fixed here.


On left comment #7981 on Lemma 90.3.12 in Formal Deformation Theory

Thanks and fixed here.


On left comment #7980 on Lemma 10.35.4 in Commutative Algebra

Well, we proved that every nonempty open of contains a closed point. Going to leave this alone, unless others chime in.