Timeline for monodromy and global cohomology
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| May 4, 2010 at 5:03 | vote | accept | shenghao | ||
| May 3, 2010 at 23:41 | comment | added | Emerton | This is to do with wild ramification at infinity, a phenomenon which you can't see with local systems on Riemann surfaces. The formula for the Euler char. for an $\ell$-adic sheaf on an open curve $U$ is (rank $\mathcal L$)$\cdot \chi(U)$ minus the sum of the Swan conductors at each of the missing points. These Swan conductors measure wild ramification around each of the punctures, and can be arbitrarily large. Thus $H^1_c$ can have arbitrarily large rank in this setting. | |
| May 3, 2010 at 19:01 | comment | added | shenghao | Thanks, Matt. Long ago, de Jong told me that, if U is an affine curve over a finite field, and L ranges over all local systems on U of rank 1, then the dimension h^1_c(U,L) has no upper bound, due to arbitrary ramification at infinity. I'm trying to convice myself why it is so. Is it something special about finite field, like the Artin-Schreier cover? | |
| May 3, 2010 at 17:14 | history | edited | David Zureick-Brown | CC BY-SA 2.5 |
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| May 3, 2010 at 15:34 | history | answered | Emerton | CC BY-SA 2.5 |