Timeline for p-adic Langlands in Families
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Apr 4, 2011 at 2:46 | comment | added | Emerton | Dear Kevin, When considering the behaviour of the (classical) local Langlands correspondence in families, I think it is better to replace the correspondence as usually considered by the Breuil--Schneider correspondence, in which non-generic representations are replaced by the parabolic inductions of which they are the Langlands quotient. (This is discussed in my recent preprint with David Helm, for example.) I should add that the behaviour of this modified correspondence in families is still quite subtle (and this is the subject of my preprint with David). Best wishes, Matt | |
| Apr 4, 2011 at 0:59 | answer | added | Emerton | timeline score: 8 | |
| Apr 3, 2011 at 22:56 | comment | added | Kevin Buzzard | I will remark that the classical local Langlands correspondence does not behave well in families. For if you consider a reducible representation $\chi_1\oplus\chi_2$ and then let $\chi_1$ and $\chi_2$ vary in a complex family, then occasionally $\chi_1/\chi_2$ can be $|.|^{\pm1}$ and in these cases the associated $\pi$ is 1-dimensional, so even the dimension of $\pi$ jumps. | |
| Apr 3, 2011 at 22:23 | history | asked | Anonymous | CC BY-SA 2.5 |