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Comments 1 to 20 out of 5160 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 PLACEMENT TRAINING left comment #5545 on Lemma 85.18.10 in Formal Algebraic Spaces

Can’t tell a good article, because it is more than that, thanks keep going... PLACEMENT TRAINING https://www.gobrainwiz.in/pages/crt


On left comment #5544 on Section 4.22 in Categories

But it is enough to suppose that is a (co-)cone of the diagram, and this observation is actually important in Lemma 05SH, as this lemma is (rightly) formulated without any exactness conditions on . Such conditions are not needed because any functor preserves (co-)cones even if it does not preserve (co-)limits.


On Harry Gindi left comment #5543 on Lemma 58.73.3 in Étale Cohomology

The corresponding lemma in SGA4 (IX.2.14) asserts (1) for a map F into the product rather than the coproduct. Is this a typo?


On Zhenhua Wu left comment #5540 on Lemma 29.40.8 in Morphisms of Schemes

Locally of finite type will suffice as universally closed morphism is quasi-compact, it's best to change this description in order to be consistent with tag 0AH6.


On minsom left comment #5539 on Section 17.12 in Sheaves of Modules

May I ask you something? In the proof of lemma 01BY (3) , how can we show that "There exists an open covering of such that on each open all the sections lift to sections of ." ? For sheaf axiom , we need the fact ' for open cover , , each element is same in '


On Michael left comment #5538 on Lemma 29.55.5 in Morphisms of Schemes

It looks like there is a typo here. should be and similiarly for . There is a total of three occurrences.


On David Liu left comment #5537 on Section 30.12 in Cohomology of Schemes

In the proof of lemma 01YH, why does and have supports that are strictly contained in ?


On Zeyn Sahilliogullari left comment #5536 on Lemma 26.11.5 in Schemes

g∈A in the second to last sentence should be g∈B


On left comment #5535 on Lemma 43.22.1 in Intersection Theory

The reference is not precise. I think it is better to write [Chapter V, C), Section 7, formula (10), Serre_algebre_locale]


On left comment #5534 on Lemma 42.25.3 in Chow Homology and Chern Classes

In the statement of the Lemma 02ST, I believe the last line should be .


On left comment #5533 on Lemma 42.25.3 in Chow Homology and Chern Classes

In the statement of the Lemma 02ST, I believe the last line should be .


On Chi Zhang left comment #5532 on Lemma 26.17.5 in Schemes

Maybe $\mathfrak{p}$ is more precisely a maximal ideal? Since it is the kernel of the ring morphism $\kappa(x)\otimes_{\kappa(x)}\kappa(y)\to \kappa(z)$.

On left comment #5531 on Definition 10.87.7 in Commutative Algebra

Yes, but the condition is independent of the choice by part (1) of the proposition.


On Dion Leijnse left comment #5530 on Lemma 48.2.1 in Duality for Schemes

In part (2) of the statement of the Lemma, I think the $K|_U$ should be $K|_{U_i}$.

On left comment #5529 on Lemma 15.63.10 in More on Algebra

Lemma needs "Assume B is flat as an A-module".


On Roman Bezrukavnikov left comment #5528 on Definition 10.87.7 in Commutative Algebra

In Proposition 059E we a given a module M and a directed system having M as a limit, while in this definition we are only given a module. Is the meaning here that there exists a directed system for which equivalent conditions of the Proposition hold?


On Kang Taeyeoup left comment #5527 on Section 26.7 in Schemes

Alternatively, I believe that the proof can be done by much easier and elegant way.

We have a Hom-Tensor adjuntion in the category of -modules.

Using this with the lemma 26.7.1, we get the following bunch of natural isomorphisms.

Since this hold for any , we have that .


On Kang Taeyeoup left comment #5526 on Section 26.7 in Schemes

I think the first proof of the lemma 01I8 a) is not clear. The proof shows that there is the isomorhpism , and this gives the corresponding isomorphism

However, an adjunction does not guarantee that the isomorphisms in the one part goes to isomorphisms in the other part.

Suppose and are given and is left adjoint to .

Let be an isomorphism, then the corresponding morphism in is given by the composite . Here is a counit. In general there is noreason that should be an isomorphism.


On Wen-Wei LI left comment #5525 on Lemma 13.18.7 in Derived Categories

Extra ) in the last displayed formula of this proof.


On Olivier de Gaay Fortman left comment #5524 on Lemma 92.18.2 in Algebraic Stacks

I think you mean by Algebraic-Stacks/S the 2-category of algebraic stacks over , defined using , and similarly for Algebraic-Stacks'/S.