Timeline for Purity of vanishing cycle for proper scheme over DVR with smooth generic fiber
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Aug 27, 2019 at 20:21 | history | bounty ended | Zhiyu | ||
| S Aug 27, 2019 at 20:21 | history | notice removed | Zhiyu | ||
| Aug 23, 2019 at 19:42 | answer | added | Will Sawin | timeline score: 4 | |
| Aug 23, 2019 at 18:37 | comment | added | Zhiyu | @user45878 Can you give a reference? | |
| S Aug 23, 2019 at 18:36 | history | bounty started | Zhiyu | ||
| S Aug 23, 2019 at 18:36 | history | notice added | Zhiyu | Draw attention | |
| Aug 23, 2019 at 18:35 | comment | added | Zhiyu | @DonuArapura Thank you! Do you know any example that the vanishing cycle sheaf is not pure? | |
| Aug 23, 2019 at 16:50 | comment | added | Pol van Hoften | No to both questions, but I think it should be true that $H^i$ always has weights $\le 2i$. | |
| Aug 23, 2019 at 12:50 | comment | added | Donu Arapura | Added: Weil II only talks about the equicharacteristic case. I don't know the state of the art in general. | |
| Aug 23, 2019 at 12:44 | comment | added | Donu Arapura | No, the cohomology of $R \Phi \mathbb{Q}_l$ wouldn't be pure in general. The vanishing cycle sheaf is mixed. It carries a monodromy weight filtration with respect to which the associated graded is pure. Look at Weil II for more details. | |
| Aug 23, 2019 at 0:04 | history | edited | Zhiyu | CC BY-SA 4.0 |
added 109 characters in body; edited tags
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| Aug 21, 2019 at 20:26 | history | edited | Zhiyu | CC BY-SA 4.0 |
make the notation more clear
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| Aug 21, 2019 at 18:27 | history | edited | Zhiyu | CC BY-SA 4.0 |
added 9 characters in body
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| Aug 21, 2019 at 17:57 | history | asked | Zhiyu | CC BY-SA 4.0 |