Comments 1 to 20 out of 6207 in reverse chronological order.


On bryce left comment #6663 on Definition 109.26.2 in Exercises

Hello Professor,

I think there is a typo: "we have $\phi(M) = \phi(M') + \phi(M')$" instead of $\phi(M) = \phi(M') + \phi(M'')$.

On Jonas Ehrhard left comment #6662 on Situation 32.4.5 in Limits of Schemes

Maybe observe that $S$ is also necessarily quasi-compact and quasi-separated in this situation? Both follows because $S \to S_0$ is affine and $S_0$ is quasi-compact and quasi-separated. Quasi-separatedness is used in 01Z4, quasi-compactness in 01Z5.

On Jonas Ehrhard left comment #6661 on Lemma 32.4.3 in Limits of Schemes

Do we need all the $S_i$ to be quasi-compact or is it sufficient to assume that $S_0$ is quasi-compact?

On Jonas Ehrhard left comment #6660 on Lemma 32.4.4 in Limits of Schemes

Should it be $S_0 = \bigcup_j U_{0, j}$ in the first sentence of the proof?

On left comment #6659 on Section 15.48 in More on Algebra

@#6657. You can do that but you don't need to do that because you can always get $a^p \in B$ by clearing denominators. Namely, if $a^p = b_1/b_2$ for $b_i \in B$ with $b_2$ nonzero, then you have $(b_2 a)^p \in B$.

On Jonas Ehrhard left comment #6658 on Lemma 32.4.1 in Limits of Schemes

Typo in the third sentence of the proof: it should be transition instead of transtion.

On 国蝻 left comment #6657 on Section 15.48 in More on Algebra

I think there is still one point in the proof of lemma 07PI: Assume that K=M[a] with a\in A, to guarantee that a^p\in B I think it is better to take B as the integral closure of A in M.

On 国蝻 left comment #6656 on Section 15.48 in More on Algebra

@ Johan Yes I totally agree. Thank you very much.

On left comment #6655 on Section 15.48 in More on Algebra

@国蝻 Yes, good question! I guess I should have said that we may and do choose $z$ to be an element of $A$. We apply Lemma 15.48.4 to the ring extension $A' = B[z]/(z^p - b)$ of $B$ and we see that $A'$ is J-0. Then $A' \subset A$ induces an isomorphism of fraction fields. Hence $A$ is J-0 by Lemma 15.47.5. Do you agree?

On 国蝻 left comment #6654 on Section 15.48 in More on Algebra

I'm sorry but how can I deduce that A=B[z]/(z^p-b) or A\subset B[z]/(z^p-b) in the proof of lemma 07PI? (So we can use lemma07PG or lemma07PA ?)

On Akhil Mathew left comment #6653 on Section 32.8 in Limits of Schemes

Does the reference at the end of the proof of Lemma 32.8.15 (Lemma 0C3L) mean to point somewhere else (currently to 07BV)?

On Brian Shin left comment #6652 on Lemma 37.55.12 in More on Morphisms

Very small typo: $i_*\mathcal{O}_X$ should be $i_*\mathcal{O}_Z$

On 七海辣辣米 left comment #6651 on Section 10.108 in Commutative Algebra

In lemma 04PU, the first line, 'by going up' should be 'by going down'.

On Likun Xie left comment #6650 on Section 10.63 in Commutative Algebra

Lemma 10.63.13, don't we need $M$ to be finite over $S$? Proposition 10.63.6 is for finite module.

On left comment #6649 on Lemma 48.18.2 in Duality for Schemes

pelajaran apa ini gak paham aku \ref{https://en.gravatar.com/galuhmaheswara/}

On 七海辣辣米 left comment #6648 on Lemma 10.108.2 in Commutative Algebra

In lemma 04PS, the first paragraph, there is a missed 0 in the second exact sequence.

On Phoebe left comment #6647 on Lemma 29.43.16 in Morphisms of Schemes

Oh I was being stupid. I get it now. You can delete my comments.

On Phoebe left comment #6646 on Lemma 29.43.16 in Morphisms of Schemes

Why does $\textbf{P}(\mathcal{E})=\textbf{P}(\mathcal{E}\otimes_{\mathcal{O}_S}\mathcal{L}^{\otimes n})$ follow from Lemma 27.20.1?

On Laurent Moret-Bailly left comment #6645 on Lemma 33.42.8 in Varieties

For condition (6) one could of course weaken the assumption "If $k$ is perfect" to "If $\kappa(x)/k$ is separable".

On WhatJiaranEatsTonight left comment #6644 on Lemma 42.29.5 in Chow Homology and Chern Classes

In the last row of the statement, gysin map should be Gysin map.