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Comments 1 to 20 out of 8413 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 #9031 on Lemma 59.73.13 in Étale Cohomology

This blog post offers a concise explanation of the properties related to the inclusion maps of schemes in algebraic geometry. The clarity in defining the behavior of E under the inclusions g and j is appreciated, especially with the solid backing of algebraic lemmas and theorems. It's always refreshing to see complex concepts like these broken down with such precision. Great read for anyone delving into the specifics of scheme theory!

On left comment #9030 on Lemma 59.73.13 in Étale Cohomology

Thanks for sharing this information. I really like your blog post very much. You have really shared a informative and interesting blog post with people. website : KINGDOM357

On left comment #9029 on Lemma 59.73.13 in Étale Cohomology

Thanks for sharing this information. I really like your blog post very much. You have really shared a informative and interesting blog post with people. website : KINGDOM357

On DU Changjiang left comment #9028 on Lemma 59.73.13 in Étale Cohomology

there is a typo in the proof: in the third line, a right parenthesis is missing. The right one should be

On João Candeias left comment #9027 on Lemma 9.8.9 in Fields

I think this is still not quite correct, as a countable product of countables is not countable (already a countable product of finite sets isn't countable), so in particular if we take , we see that a countable product of copies of has bigger cadinality than that of (which is equal to ). Hence this is not a valid argument.

However, we are only interested in a subset of , which can be obtained as a countable union (all possible degrees ) of finite products (all possible coefficients of the polynomial) of , and this is indeed bounded by .

On James left comment #9026 on Lemma 92.10.2 in The Cotangent Complex

"zero" is repeated twice in the 3rd line of the proof.

On Liam left comment #9025 on Section 26.21 in Schemes

In the proof of Lemma 26.21.7 (b), it's not obvious that the collection of U V forms an open cover, however, we can check this easily by checking that every k-point is in one of this collection for every field.

On Zheng Yang left comment #9024 on Section 10.134 in Commutative Algebra

There is a typo below Defn. 07BN in the description of the cotangent complex. The sentence should be corrected to read: "... the chain complex associated to the simplicial module..."

On jack left comment #9023 on Remark 10.78.4 in Commutative Algebra

Here the formula defining R is recursive, but it should just be C^\inft(\mathbb{R}) of course. 052H has the same problem since it is a copy of this.

On Zhenhua Wu left comment #9022 on Lemma 9.16.3 in Fields

In the last line, the function should be .

On left comment #9021 on Section 12.6 in Homological Algebra

@#8412 Thanks and fixed here.

On left comment #9020 on Lemma 10.153.3 in Commutative Algebra

Thanks to the comments 8410, 8561, 8796, 8797. Fixed here.

On left comment #9019 on Section 10.36 in Commutative Algebra

Thanks and fixed here.

On left comment #9018 on Proposition 13.16.8 in Derived Categories

Thanks, this is indeed better. Fixed here.

On left comment #9017 on Theorem 58.6.2 in Fundamental Groups of Schemes

Hahaha! Yes, of course. The notation is that is the map between groups and that the functor between the categories of sets with group actions is supposed to be induced by . See Lemma 58.3.11. Going to leave as is for now.

On Zhenhua Wu left comment #9016 on Lemma 9.16.6 in Fields

The part ''It follows from Lemma 09HQ that is normal over and that it is the smallest normal subextension of containing needs clarification. To be specific: 1)why is an field; 2)how do we use lemma 09HQ to show is normal; 3) how do we show that it is the smallest normal subextension of containing .

On James left comment #9015 on Section 105.7 in Introducing Algebraic Stacks

Another mistake (mine of course): the dimension calculation above is 6-5. Apologies for the spam.

On left comment #9014 on Lemma 13.16.7 in Derived Categories

Thanks and fixed here.

On left comment #9013 on Lemma 13.16.5 in Derived Categories

Thanks and fixed here.

On left comment #9012 on Lemma 13.16.3 in Derived Categories

Thanks! I fixed it in a slightly different way because it suffered from the same pitfall as the previous lemma. See changes.


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