Timeline for Katz Modular Functions and Emerton's Completed Cohomology
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jun 24, 2011 at 23:23 | vote | accept | ndk | ||
| Jun 24, 2011 at 23:23 | |||||
| Jun 22, 2011 at 19:56 | history | edited | Kevin Buzzard | CC BY-SA 3.0 |
typo :-/
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| Jun 22, 2011 at 19:55 | comment | added | Kevin Buzzard | classical Hodge Theory. On the other hand I still find it a little surprising that one "only" needs to adjoin all roots of unity and then complete -- I should look at the paper more closely. I guess Tate got away with adjoining all $p$-power roots of unity and completing in his $p$-divisible groups paper though, so perhaps I shouldn't be so surprised. | |
| Jun 22, 2011 at 19:53 | comment | added | Kevin Buzzard | Olivier -- thanks for bringing this paper to my attention -- I was unaware of it. Although I've only taken a superficial glance at it, it seems to me that Ohta does not do what the OP wants: the OP specifically wants something over $\mathbf{Z}_p$ (this is my reading of the question). Ohta base changes to the integers of a p-adically complete field containing all roots of unity, and such an integer ring must be very far from $\mathbf{Z}_p$. Somehow it's less surprising that one can do something now, because one is closer to being able to use $p$-adic Hodge theory to replace Shimura's... | |
| Jun 22, 2011 at 17:20 | comment | added | Olivier | Sure. M.Ohta On the p-adic Eichler-Shimura isomorphism for $\Lambda$-adic cusp forms (Crelle 463)+the fact that the Hecke algebra is complete intersection (under the assumptions that you know) thanks to Wiles/Taylor-Wiles to have a canonical splitting of the short exact sequence Ohta considers. | |
| Jun 22, 2011 at 15:46 | comment | added | Kevin Buzzard | Olivier -- I know of no such Eichler-Shimura map, even in the ordinary case. Can you give a precise reference? | |
| Jun 22, 2011 at 8:23 | comment | added | Olivier | Doesn't part of this works at least in the ordinary case though? Say the ordinary Hecke algebra is Gorenstein, then I think you do have such a canonical Eichler-Shimura map by the work of Mazur-Wiles and Ohta. All in all, this seems to me to indicate that indeed any natural such map will live in some $p$-adi period space, which happens to be your ring of coefficients in the ordinary case, so I guess I share the general pessimism. | |
| Jun 22, 2011 at 6:08 | vote | accept | ndk | ||
| Jun 22, 2011 at 6:08 | |||||
| Jun 22, 2011 at 5:36 | history | answered | Kevin Buzzard | CC BY-SA 3.0 |