The Stacks project

Comments 1661 to 1680 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 #7959 on Lemma 10.147.2 in Commutative Algebra

Thanks and fixed here.

On left comment #7958 on Lemma 10.147.1 in Commutative Algebra

Thanks and fixed here.

On left comment #7957 on Lemma 37.19.2 in More on Morphisms

Thanks and fixed here.

On left comment #7956 on Lemma 67.49.1 in Morphisms of Algebraic Spaces

THanks and fixed here.

On left comment #7955 on Example 65.14.2 in Algebraic Spaces

Thanks. Fixed here.

On R left comment #7954 on Lemma 107.5.18 in The Geometry of Algebraic Stacks

The statement should probably read "locally Noetherian algebraic stacks" instead of "locally Noetherian schemes".

On LSpice left comment #7953 on Section 12.6 in Homological Algebra

"An morphism of extensions" should be "A morphism of extensions".

On Raffaele Lamagna left comment #7952 on Lemma 27.15.5 in Constructions of Schemes

in the commutative diagram is not defined.

On Owen left comment #7948 on Lemma 59.75.6 in Étale Cohomology

This lemma holds without any noetherian hypothesis on if the stalks of are supposed of finite presentation. Also it holds with no assumptions on or if is supposed constructible (SGA 4 IX Proposition 2.11 – the definition of constructible there requires the stalks to be of finite presentation).

On Laurent Moret-Bailly left comment #7947 on Lemma 54.4.3 in Resolution of Surfaces

Typo in last sentence of statement: "is the blowing up".

On Laurent Moret-Bailly left comment #7946 on Lemma 54.4.1 in Resolution of Surfaces

The notation from the statement is not used, and means something else in the proof. Also, (although easy to guess) is not defined.

On Haohao Liu left comment #7945 on Lemma 48.27.1 in Duality for Schemes

In item (2), should be ?

On 11k left comment #7944 on Lemma 42.46.2 in Chow Homology and Chern Classes

I think and be replaced by and . The same changes apply to that on .

On Nico left comment #7943 on Lemma 33.35.3 in Varieties

Tiny typo. Where it says "the intersection is a proper -subvector space", the set should be replaced by its span.

On Laurent Moret-Bailly left comment #7942 on Theorem 89.8.3 in Resolution of Surfaces Revisited

Punctuation missing at the end of line 2 of statement.

Also, the phrasing of (4) is strange (especially "such that"). The condition should be something like:
" is finite, and is a finite set, and for each the completed local ring of is normal".

On left comment #7940 on Lemma 31.9.6 in Divisors

Seemingly the last part should be put into the enumerate-environment since you refer to it as (4) in the proof.

On left comment #7939 on Lemma 87.35.3 in Formal Algebraic Spaces

Is there a typo in the sentence "Our goal is to show that .... is zero for ." Should be ?

On left comment #7938 on Lemma 47.3.5 in Dualizing Complexes

This proof seems to adapt to any Grothendieck abelian category. A reference for this general statement: Lurie, Spectral Algebraic Geometry, Lemma C.5.6.4.

On 11k left comment #7937 on Lemma 42.41.4 in Chow Homology and Chern Classes

Is ampleness of redundant?

On Karl Schwede left comment #7936 on Section 20.27 in Cohomology of Sheaves

For Lemma 079U, presumably should be in ?


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