Timeline for Correspondences acting on cohomology groups $H^*(X)$ & splittings
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 27, 2023 at 10:33 | vote | accept | JackYo | ||
| May 31, 2023 at 14:30 | answer | added | Dan Petersen | timeline score: 2 | |
| May 31, 2023 at 14:28 | answer | added | Will Sawin | timeline score: 3 | |
| May 31, 2023 at 3:33 | comment | added | JackYo | @WillSawin: I not understand how to see that $D \times X $ gives idempotent endomorphism if we assume that $D$ has degree one as Q-divisor, Could you sketch the argument? | |
| May 30, 2023 at 20:09 | comment | added | Will Sawin | Sufficient for what? It's easy to calculate the composition to check that $D \times X$ is idempotent, and every idempotent gives a splitting. | |
| May 30, 2023 at 19:28 | history | edited | JackYo | CC BY-SA 4.0 |
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| May 30, 2023 at 19:28 | comment | added | JackYo | (yes, $X$ can be assumed as proper) | |
| May 30, 2023 at 19:25 | comment | added | JackYo | @WillSawin: But is degree $1$ assumption also sufficeient? Intuitively it's not obvious to me, but it seems that's what Dan Petersen used (compare with comment #4 in the linked discussion below the answer). It seems that he took an arbitrary effective divisor, divided it's degee in order to norm it's degree to one, and this should already give the splitting. | |
| May 30, 2023 at 19:07 | comment | added | Will Sawin | Certainly $D \times X$ is an idempotent endomorphism and $X \times D $ is another idempotent endomorphism if $X$ is proper (or maybe, depending on conventions, the other way around). The degree $D$ being one is necessary to get idempotence. Otherwise you would get the relation $E^2 = E \cdot \deg D$ for $E$ the endomporphism. | |
| May 30, 2023 at 18:17 | history | edited | JackYo | CC BY-SA 4.0 |
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| May 30, 2023 at 17:59 | history | edited | JackYo | CC BY-SA 4.0 |
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| May 30, 2023 at 17:51 | history | edited | JackYo | CC BY-SA 4.0 |
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| May 30, 2023 at 17:44 | history | asked | JackYo | CC BY-SA 4.0 |