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Comments 1 to 20 out of 4992 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 BCnrd left comment #5364 on Lemma 39.9.9 in Groupoid Schemes

Should assume (so ) or else "only if" is not true (fails when ). Maybe also replace "" with "", to avoid awkward-looking notation such as .


On MAO Zhouhang left comment #5363 on Lemma 15.29.4 in More on Algebra

A typo in the hypothesis of the second statement: the second sequence should be , not .


On Mike Shulman left comment #5362 on Definition 7.29.2 in Sites and Sheaves

"Dense morphism"? (cf. e.g. section 11 of my paper http://www.tac.mta.ca/tac/volumes/27/7/27-07abs.html, which may not be exactly the same but is very closely related)


On Anh left comment #5361 on Section 10.119 in Commutative Algebra

What is the definition of height 1 prime ideal? Please help me I don't understand.


On Laurent Moret-Bailly left comment #5360 on Lemma 58.66.1 in Étale Cohomology

In addition to Ben's comment, the converse (constructing from ) is proved but not stated. Also, in the proof there are 3 instances of an exponent standing for .


On Anh left comment #5359 on Section 10.119 in Commutative Algebra

What is the definition of height 1 prime ideal? Please help me I don't understand.


On MAO Zhouhang left comment #5358 on Section 47.8 in Dualizing Complexes

It might be better to either mention that the definition of is a special case of the one in that section about Serre subcategories, or incorporate a specialized definition here.


On MAO Zhouhang left comment #5357 on Section 47.12 in Dualizing Complexes

It might be better to mention the name (Matlis)-Greenless-May duality in the text or in the slogan, which facilitates searching and locating.


On Peter Bruin left comment #5356 on Lemma 10.55.1 in Commutative Algebra

In the proof of (1), shouldn't be ?


On Ben Moonen left comment #5355 on Section 58.66 in Étale Cohomology

Hi Johan, In the statement of Lemma 0DV7 there is no relation between the sheaves F and G, which is not per se wrong but looks funny. Maybe better to make the statement more explicit, matching its proof: if G has cohomology then so does F = g^{-1}G; if F has cohomology then so does G = g_*F. Best wishes, Ben


On Zhenhua Wu left comment #5354 on Section 39.6 in Groupoid Schemes

tag 047I. Sorry for spam, the input of asterisk keeps bugging. This is my last try. The assumption of flatness is not needed for the result. See Prop (3.15) of "abelian varieties" by Ben Moonen. In short, define which is an automorphism. Denote as the left projection and by the right one. So we have an isomorphism: Let , so we have Q.E.D.


On Zhenhua Wu left comment #5353 on Section 39.6 in Groupoid Schemes

tag 047I. The assumption of flatness is not needed for the result. See Prop (3.15) of this link \ref{http://page.mi.fu-berlin.de/elenalavanda/BMoonen.pdf} In short, define which is an automorphism. Denote as the left projection and by the right one. So we have an isomorphism: Let , so we have Q.E.D.


On Zhenhua Wu left comment #5352 on Section 39.6 in Groupoid Schemes

tag 047I. The assumption of flatness is not needed for the result. See Prop (3.15) of this link \ref{http://page.mi.fu-berlin.de/elenalavanda/BMoonen.pdf}Define. In short, define which is an automorphism. Denote as the left projection and by the right one. So we have an isomorphism: Let , so we have Q.E.D.


On Noah Olander left comment #5351 on Section 22.4 in Differential Graded Algebra

Shouldn't a right -module be the same as a map , not as you have written? It's possible that I'm misremembering a sign convention but this seems not right.


On Jackson left comment #5350 on Lemma 57.10.2 in Fundamental Groups of Schemes

Shouldn't the extension of be a morphism over ?


On left comment #5349 on Section 9.26 in Fields

In the fourth paragraph of the proof of Lemma 030F you should say that B * is algebraically independent over F, not on E.


On Will Chen left comment #5348 on Section 96.11 in Artin's Axioms

After "We spell out what this means", I think the 's should be


On Hao left comment #5347 on Lemma 37.17.3 in More on Morphisms

It's better to mention what is in Lemma 07TD.


On Anton Güthge left comment #5346 on Section 58.15 in Étale Cohomology

Typo: in 03NY (5), I think either both or non of the inclusions i_x and i_y should be written with a hooked arrow


On left comment #5345 on Lemma 56.9.8 in Derived Categories of Varieties

Again thanks. I have now fixed this here in exactly the manner you suggested.