Timeline for Is there a "trianguline period ring", or is one expected?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 14, 2011 at 16:27 | vote | accept | David Hansen | ||
| Jul 14, 2011 at 10:43 | comment | added | Laurent Berger | Of course, there's also the fact that a representation is trianguline if the matrices of $\phi$ and $\gamma$ on its $(\phi,\Gamma)$-module are upper triangular. | |
| Jul 14, 2011 at 10:42 | comment | added | Laurent Berger | Colmez invented it. Here are the man's own words "Le triangle est un instrument de musique dont le son (triangulin (?)) est presque cristallin... ". | |
| Jul 14, 2011 at 7:17 | comment | added | Mariano Suárez-Álvarez | Who came up with the word "trianguline"? Maybe not everyone should be allowed to invent words...! :) | |
| Jul 14, 2011 at 6:45 | answer | added | Laurent Berger | timeline score: 14 | |
| Jul 14, 2011 at 3:36 | comment | added | David Hansen | Thanks for the remarks! Indeed, I swept the necessity of a refinement under the carpet with the word "roughly", though perhaps this was (ironically) too rough. | |
| Jul 14, 2011 at 3:23 | comment | added | Emerton | If you just close up crystalline points in a local deformation space, you will get the whole space. (See Kisin's article in the 2nd p-adic Langlands volume of Asterisque.) In order to have the closure be trianguline reps. (rather than all reps.) you need to add a refinement at every point. So whatever $B$ is (if it does exist), it will involve not just a Galois representation, but a Galois representation together with a refinement. (And note that, beyond the 2-dimensional case, it's not so clear --- at least to me --- how one should define the notion of refinement.) | |
| Jul 13, 2011 at 21:08 | history | asked | David Hansen | CC BY-SA 3.0 |