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#6651 on tag 04PQ by 七海辣辣米

七海辣辣米 — Wed, 20 Oct 2021 04:02:06 GMT

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

#6650 on tag 00L9 by Likun Xie

Likun Xie — Tue, 19 Oct 2021 09:42:28 GMT

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

#6649 on tag 0FWI by Media Online

Media Online — Tue, 19 Oct 2021 06:11:35 GMT

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#6648 on tag 04PS by 七海辣辣米

七海辣辣米 — Tue, 19 Oct 2021 08:14:16 GMT

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

#6647 on tag 087S by Phoebe

Phoebe — Tue, 12 Oct 2021 07:28:57 GMT

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

#6646 on tag 087S by Phoebe

Phoebe — Tue, 12 Oct 2021 05:09:45 GMT

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

#6645 on tag 0B8Y by Laurent Moret-Bailly

Laurent Moret-Bailly — Tue, 12 Oct 2021 02:14:20 GMT

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

#6644 on tag 0B73 by WhatJiaranEatsTonight

WhatJiaranEatsTonight — Sat, 09 Oct 2021 02:48:47 GMT

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

#6643 on tag 02TM by WhatJiaranEatsTonight

WhatJiaranEatsTonight — Sat, 09 Oct 2021 02:26:35 GMT

I think the equation in the statement should be $i^*div_N(t)=c_1(N|_D)\cap[D]$ . Otherwise, the element in the right is an element in $CH_{n-2}(X)$ .(Though they are equal in the cycle level.)

#6642 on tag 02SU by WhatJiaranEatsTonight

WhatJiaranEatsTonight — Fri, 08 Oct 2021 07:48:49 GMT

I do not know why it need to construct $X'$ and $Y'$ . Can we reduce the conclusion to $X,Y$ integral merely by the linearity of two sides of the equation?

Does the requirement of the cycles to be "locally finite" but not "finite" matter?