Timeline for Reference for cdh topology
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Jan 26, 2015 at 9:44 | comment | added | Matthias Wendt | Sorry, I only know references related to motivic cohomology or homotopy, nothing in a general way... | |
| Jan 25, 2015 at 21:21 | comment | added | Heer | @Matthias and Mikhail thank both of you for clarifying the definition! Do you happen to know some good reference for cdh topology? | |
| Jan 25, 2015 at 19:43 | comment | added | Matthias Wendt | (Sorry, I used the notation of the Wikipedia article) The point is that the closed subset over which $f$ is not an isomorphism is a necessary part of the covering. In particular, the exact sequence you are asking for should have $\operatorname{Pic}(Y)\to\operatorname{Pic}(X)\oplus\operatorname{Pic}(Z)$ with $Z$ the complement of $U$. | |
| Jan 25, 2015 at 17:48 | comment | added | Heer | won't $f（X-U）\rightarrow Y$ give such a closed immersion? Note: i stick to my old notation, which is opposite to yours, X--〉Y | |
| Jan 25, 2015 at 16:35 | comment | added | Matthias Wendt | In the Wikipedia article, the cdh-covering is the proper map $p:Y\to X$ together with the closed immersion $e:A\to X$. This way, each point of $X$ has a point lying above it with isomorphic residue field. | |
| Jan 25, 2015 at 12:59 | comment | added | Heer | now i am confused. According to wiki page for h-topology, this is just the example of cdh-cover given there | |
| Jan 25, 2015 at 9:00 | comment | added | Mikhail Bondarko | I believe that a proper generically surjective morphism is always surjective. Yet it not clear that above any point $y$ of $Y$ there is an isomorphic point $x$ of $X$ (so, the question is whether the field for $x$ is isomorphic to that for $y$ and not just a finite extension of it). | |
| Jan 25, 2015 at 8:53 | history | edited | Heer | CC BY-SA 3.0 |
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| Jan 25, 2015 at 8:52 | comment | added | Heer | no, thanks for that point. i guess i need f to be surjective. i have edited my question | |
| Jan 24, 2015 at 21:44 | comment | added | Mikhail Bondarko | Are you sure that all (non-generic) points of $Y$ lift to $X$? | |
| Jan 24, 2015 at 20:00 | history | edited | Heer | CC BY-SA 3.0 |
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| Jan 24, 2015 at 19:23 | history | edited | Heer | CC BY-SA 3.0 |
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| Jan 24, 2015 at 19:22 | comment | added | Heer | i made a very stupid mistake, now i have editted my question. | |
| Jan 24, 2015 at 16:57 | history | asked | Heer | CC BY-SA 3.0 |