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\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 Anonymus left comment #10115 on Lemma 59.91.5 in Étale Cohomology

I believe that at this stage, you still allow to be a sheaf of sets, so you probably do not wish to speak of "groups" in the second to last sentence. Perhaps I overlook something, but I also do not understand the reference to 0A3I. Isn't the proof already complete before (apart from the question of compatibility of the relevant maps)?

On left comment #10114 on Section 6.11 in Sheaves on Spaces

Okay, this is some serious math stuff! Stalks of presheaves... Definitely not light reading, but it seems pretty fundamental if you're into topology and category theory. Good examples helped a bit!

On left comment #10113 on Lemma 15.86.7 in More on Algebra

@#9964: Instead of #9963, invoke 13.34.2.

On left comment #10112 on Lemma 19.13.4 in Injectives

@#9963 Sorry, apparently this result was already included: it's 13.34.2.

On Shubhankar left comment #10111 on Theorem 59.91.11 in Étale Cohomology

It seems that it would be useful to mark this theorem as 'The' proper base change theorem. More precisely, right now this statement is buried under a lot of lemmas in the section on proper base change, so it would be better to highlight it somehow.

On left comment #10110 on Lemma 15.108.6 in More on Algebra

A justification is missing as to why we can replace by with such that surjects on . Here is one: First, is a unit in , thus there is a map . This is a local ring homorphism or local rings satisfying the hypotheses of Lemma 0AGX. Thus it induces an isomorphism on completions.

On left comment #10109 on Lemma 15.108.4 in More on Algebra

Two comments:

i) The justification of why we can factor the map via is missing. One possibility is by Lemma 09XI(2) applied to the Henselian pair and the etale map . ii) The justification of why we can replace and by and respectively is missing. One possibility is because and have the same -adic completion.

On Monte left comment #10108 on Section 26.15 in Schemes

I am wondering if the following variation to Lemma 26.15.4 is true:

F, a contravariant functor from affine schemes to sets, is representable by a scheme (not necessarily affine) if the same assumptions hold in the context of F being only defined over affine schemes.

I have heard that this variation is indeed true, but I can't seem to find it written anywhere. I even skimmed EGA 1, but with my poor french I may have missed it.

On hizerain left comment #10107 on Section 106.14 in More on Morphisms of Stacks

Small typo in the introduction: 'to esthablish' should be 'to establish'

On left comment #10106 on Lemma 15.9.10 in More on Algebra

I agree with Brian Conrad's original comment, and thus swapping again is needed.

On left comment #10105 on Lemma 15.9.8 in More on Algebra

The proof can be simplified if we take to be the kernel of .

On left comment #10104 on Remark 13.19.5 in Derived Categories

primary goal is to ensure the highest level of comfort and safety during your dental treatment thanks

On left comment #10103 on Remark 13.19.5 in Derived Categories

primary goal is to ensure the highest level of comfort and safety during your dental treatment thanks

On left comment #10102 on Remark 13.19.5 in Derived Categories

primary goal is to ensure the highest level of comfort and safety during your dental treatment thanks

On left comment #10101 on Remark 13.19.5 in Derived Categories

At DCI primary goal is to ensure the highest level of comfort and safety during your dental treatment thanks

On left comment #10100 on Remark 13.19.5 in Derived Categories

At DCI –{https://charugh.ir} primary goal is to ensure the highest level of comfort and safety during your dental treatment thanks

On left comment #10099 on Remark 13.19.5 in Derived Categories

At DCI – \ref{charugh.ir}} our primary goal is to ensure the highest level of comfort and safety during your dental treatment

On Francesco Minnocci left comment #10098 on Section 41.9 in Étale Morphisms of Schemes

On second thought, fiat in Latin literally translates to "let it be done", and I just learned that by fiat is an expression meaning "imposed from above" (indeed, it is also used elsewhere on this site with the same intention).

On Francesco Minnocci left comment #10097 on Section 41.9 in Étale Morphisms of Schemes

I guess what they mean is "The property (of a morphism) of being flat is, by definition, ..." as it is given by a condition on stalks.

On Francesco Minnocci left comment #10096 on Section 29.41 in Morphisms of Schemes

@Avraham See https://stacks.math.columbia.edu/tag/05LB for a counterexample.


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