Timeline for Relationship between topological cohomology and $\ell$-adic cohomology
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 10, 2010 at 5:24 | vote | accept | josh_whitney | ||
| Aug 1, 2010 at 6:49 | history | edited | Torsten Ekedahl | CC BY-SA 2.5 |
Added clarifications
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| Aug 1, 2010 at 1:28 | comment | added | Victor Protsak | OK, my attempt at deadpan humor has spectacularly failed :( | |
| Jul 31, 2010 at 14:51 | comment | added | BCnrd | Victor, as I mentioned elsewhere, as far as I know, the general Artin comparison isomorphism (for both higher direct images and higher direct images with proper supports, no smoothness hypotheses) is only proved in the published literature for torsion coefficients. The content for the $\ell$-adic case is a certain compatibility with inverse limits of sheaves entirely on the topological side (allowing constructible coefficients). My impression is that every expert works out an argument for themself, but I would be happy if someone could point to a published reference with a proof. Torsten? | |
| Jul 31, 2010 at 8:03 | comment | added | Victor Protsak | I thought that one of the greatest benefits of MO was that BCnrd would save every lost soul from wading through thousands of pages of EGA/SGA by instantaneously pinpointing the right section, together with all the errors and ways to correct them! | |
| Jul 31, 2010 at 6:33 | comment | added | BCnrd | Awesome, so this would take of my concern about effectivity (and eliminate the relevance of fancier base change theorems). That is, I assume for the various strata there's a combinatorially computable invariant which determines smoothness even when the base isn't a field, and so the above geometric structure would then assure such smoothness determination identifies exactly the characteristics away from which the desired result holds. | |
| Jul 31, 2010 at 6:10 | history | answered | Torsten Ekedahl | CC BY-SA 2.5 |