Timeline for Automorphic forms and Galois representations over imaginary quadratic fields: generalizing Taylor's theorem?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 6, 2011 at 15:48 | vote | accept | David Hansen | ||
| Jan 5, 2011 at 16:40 | comment | added | Emerton | No, it is not obvious, and therein lies the difficulty. | |
| Jan 5, 2011 at 16:24 | comment | added | David Hansen | Okay, but don't you get Eisenstein cohomology classes in this manner? Is it obvious that they're congruent modulo $\ell$-powers to cuspidal classes (which is what one would hope for in order to use pseudo-representations)? Thanks for your patience; I feel I'm missing something fundamental here. | |
| Jan 4, 2011 at 19:32 | comment | added | Emerton | If one constructs a quasi-split $GU(2,2)$ from the quad. imag. field $K$, then the hyperbolic $3$-manifolds that arise as congruence quotients for $\mathrm{GL}_2(K)$ appear in the Borel--Serre boundary of the Shimura varieties for $GU(2,2)$. | |
| Jan 4, 2011 at 19:22 | comment | added | David Hansen | Ah, interesting! What, precisely, is the natural way of moving to this Shimura variety? The form $\pi \otimes \pi^{\sigma}$ is conjugate self-dual, so should transfer, but it's not obvious to me that you could easily recover $\rho_{\pi}$ from a tensor product like this. Or am I on the wrong track? | |
| Jan 3, 2011 at 4:08 | history | answered | Emerton | CC BY-SA 2.5 |