Title: Multiplicity one for the mod p cohomology of Shimura curves
Speaker: Yongquan Hu (Morningside Center of Mathematics, CAS)
Time: 2017-6-14, 16:30—17:30
Place: 110
Abstract: At present, the mod $p$ (and $p$-adic) local Langlands correspondence is only well understood for the group $\mathrm{GL}_2(\mathbb{Q}_p)$. One of the main difficulties is that little is known about supersingular representations besides this case, and we do know that there is no simple one-to-one correspondence between representations of $\mathrm{GL}_2(K)$ with two-dimensional representations of $\mathrm{Gal}(\overline{K}/K)$, at least when $K/\mathbb{\mathbb{Q}}_p$ is (non-trivial) finite unramified.
However, the Buzzard-Diamond-Jarvis conjecture and the mod $p$ local-global compatibility for $\mathrm{GL}_2/\mathbb{Q}$ suggest that this hypothetical correspondence may be realized in the cohomology of Shimura curves with characteristic $p$ coefficients (cut out by some modular residual global representation $\bar{r}$)... (see the attachment for details)
Attachment: abstract.pdf