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Comments 1 to 20 out of 6164 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 Yuto Masamura left comment #6615 on Lemma 27.12.1 in Constructions of Schemes

Thanks for your comment, but I wanted to ask about the part of uniqueness of . More precisely, the part 'we have and and similarly for , and hence we have .'

But it's OK since I solved it by myself. At the time I misunderstood that you deduce from the first equation. The correct way is as follows: first we deduce that over and hence . Since and are the identity in degree (I overlooked this fact), we get the conclusion.


On Liu S-H left comment #6614 on Section 58.13 in Étale Cohomology

"These two are equal since by assumption and" should be ""?


On Laurent Moret-Bailly left comment #6613 on Section 15.47 in More on Algebra

About the comment following Definition 07P7: J-1 implies J-0 for nonzero reduced rings. In fact, in the rest of the section at least, the J-0 condition is considered mostly for domains. This suggests that a better definition for J-0 might be that contains a dense open.


On left comment #6612 on Section 15.47 in More on Algebra

Why is it that rings with empty Reg(X) are ruled out from being J-0? I've tried to glean from the theory here why it might be, but I think I am underinformed.

Also, doesn't the wording of Lemma 07P8 imply that J-1 rings never have an empty regular locus? (The wording: The ring R is J-1 if and only if V(𝔭)∩Reg(X) contains a nonempty open subset[...] ) I thought part of the point was that J-1 rings are allowed to have empty regular loci.


On WhatJiaranEatsTonight left comment #6611 on Lemma 42.18.3 in Chow Homology and Chern Classes

I see. The two schemes are not of the same dimension. Sorry for my ignorance.


On WhatJiaranEatsTonight left comment #6610 on Lemma 42.18.3 in Chow Homology and Chern Classes

Do I miss some details? I think that by lemma 18.1, we know that . And obviously g is a unit on . Thus .

But the proof seems much longer than I expected. I don't know if I miss some crucial details or misunderstand something.


On Yijin Wang left comment #6609 on Section 15.108 in More on Algebra

There are two typos in Lemma 0BRJ. In the first paragraph, 'Since R⊂R^{G} is an integral ring extension' should be 'Since R^{G}⊂R is an integral ring extension.' 'We may replace R by B' should be 'We may replace R^{G} by A'


On Jonas Ehrhard left comment #6608 on Section 103.5 in Introducing Algebraic Stacks

The cocycle condition for the misses a I think.


On left comment #6607 on Lemma 10.136.13 in Commutative Algebra

The point is that will be the filtered union of Noetherian rings for which the result is true. Then you use that if is a filtered colimit and if for some form a regular sequence in each for , then form a regular sequence in .


On WhatJiaranEatsTonight left comment #6606 on Lemma 10.136.13 in Commutative Algebra

(2) is equivalent to that is flat over . And since flatness is preserved under base change, we can reduce (2) to Noetherian case.

But I don't know how to reduce the case to Noetherian for (1).


On Yuto Masamura left comment #6605 on Lemma 30.14.3 in Cohomology of Schemes

@6604 Sorry, my typo: "How the map ... is obtained" should be "How is the map ... obtained".


On Yuto Masamura left comment #6604 on Lemma 30.14.3 in Cohomology of Schemes

I have a problem reading "we have a canonical isomorphism such that is the canonical map." How the map is obtained from the isomorphism ? (I think we want to say that the induced map by the map is equal to the inverse of the isomorphism , but...)


On Jonas Ehrhard left comment #6603 on Lemma 15.21.3 in More on Algebra

In the second sentence of the proof it should be (the index is missing).


On Jonas Ehrhard left comment #6602 on Lemma 10.36.2 in Commutative Algebra

Is that not just an application of Lemma 05BT to the morphism ? From there we get a polynomial with , and then .


On WhatJiaranEatsTonight left comment #6601 on Lemma 10.103.11 in Commutative Algebra

The last inequality should be . The right bracket is omitted.


On WhatJiaranEatsTonight left comment #6600 on Lemma 10.103.9 in Commutative Algebra

"Then any maximal chain of ideals". It should be "Then any maximal chain of primes".


On left comment #6599 on Definition 10.102.5 in Commutative Algebra

This from wikipedia.


On WhatJiaranEatsTonight left comment #6598 on Definition 10.102.5 in Commutative Algebra

Does means the ideal generated by the determinants of minors?


On suggestion_bot left comment #6597 on Lemma 10.115.4 in Commutative Algebra

Suggested tag: Noether normalization


On Hunter left comment #6596 on Section 5.26 in Topology

curious why "quasi-compact" is used instead of "compact" here everywhere since all spaces on the page are Hausdorff