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Comments 121 to 140 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 Jonas left comment #9776 on Lemma 10.99.4 in Commutative Algebra

For flatness of the ring map one needs to be non-zero.


On Keerthi Madapusi left comment #9775 on Section 88.30 in Algebraization of Formal Spaces

Is Lemma 30.4 missing a properness hypothesis? This is needed to invoke 087G.


On James left comment #9774 on Lemma 36.22.5 in Derived Categories of Schemes

To maintain consistency with the other statements in Tag 08ET, in the statement of the lemma it would be better to write: "the canonical map is an isomorphism."


On gad left comment #9773 on Lemma 42.67.5 in Chow Homology and Chern Classes

For the diagrams to make sense, f^ and (f')^ should be interchanged.


On left comment #9772 on Lemma 13.14.5 in Derived Categories

(Lest this comment not render properly in your browser, here is the original code.)

A proof of (1):

We have where all these colimits exist in if and only if one of them does, and where the last isomorphism comes from application of Categories, Lemma 4.17.2 to the cofinal functor (well-defined thanks to MS5; it is cofinal for it is an equivalence). The first term of these chain of isos is , whereas the last one is .


On left comment #9771 on Lemma 13.14.5 in Derived Categories

There is a slight asymmetry between the statement of (1) and (2). The former uses and the latter .


On left comment #9770 on Remark 4.22.4 in Categories

See also [KS, 7.4].


On left comment #9769 on Definition 13.14.2 in Derived Categories

An alternative reference to [SGA4, Exposé XVII] for this definition is [KS, 10.3.1], cf. also #9768.


On left comment #9768 on Remark 4.22.4 in Categories

For the interested reader, a reference for these ideas is [KS, 2.6 (specially eq. (2.6.4)), 6.1, 6.2]. An older reference is [SGA4, Exposé I, 8.4.4].


On Ana left comment #9767 on Section 37.11 in More on Morphisms

The last equation in the proof of Lemma 37.11.10 is missing a bracket ")".


On Goodluckthere left comment #9766 on Section 41.9 in Étale Morphisms of Schemes

"The property (of a morphism) of being flat is, by fiat,"

what??


On Lorenzo Mantovani left comment #9765 on Lemma 15.30.6 in More on Algebra

I believe there is a typo in the proof of this Lemma. In the second last displayed formula, the two occurrencies of the symbol should be replaced by and respectively.


On Matthieu Romagny left comment #9764 on Definition 59.15.1 in Étale Cohomology

It seems that the surjectivity condition in (1) is implied by (2).


On Branislav Sobot left comment #9763 on Lemma 15.128.4 in More on Algebra

It seems to me that you also need to choose so that it is -linearly idependent from , and then also choose to map to . Otherwise, I don't see why the obtained locus doesn't contain .


On Branislav Sobot left comment #9762 on Lemma 10.103.2 in Commutative Algebra

Sorry, but I don't see why the case can't occur. Simply take for some ideal of definition . I think that this lemma is simply wrong in this case, while the case can't occur in the next lemma.


On Sasha left comment #9761 on Section 42.54 in Chow Homology and Chern Classes

"gysin" is a name, so it should be capitalized everywhere.


On Patrick Rabau left comment #9760 on Section 5.22 in Topology

The final paragraph of the proof of Lemma 08ZY refers to Lemma 08ZN with the phrase "the intersection of all open and closed subsets of containing ". That may be ambiguously read to mean the intersection of the collection of all open sets and all closed sets containing , which is not the desired meaning. Using the usual term "clopen set" would make things shorter and clearer.


On Laurent Moret-Bailly left comment #9758 on Section 29.50 in Morphisms of Schemes

In addition to #9757, the expression birational schemes should be defined.


On Fanjun Meng left comment #9757 on Section 29.50 in Morphisms of Schemes

In the paragraph after Definition 29.50.1, it should be "the existence of a birational morphism".


On Félix left comment #9756 on Lemma 10.107.10 in Commutative Algebra

What is K in this context?