Compatibility of canonical l-adic local systems on Shimura varieties of non-abelian type
Stefan Patrikis (Ohio State University)
Abstract: Let $(G, X)$ be a Shimura datum, and let $K$ be a compact open subgroup of $G(\mathbb{A}_f)$. One hopes that under mild assumptions on $G$ and $K$, the points of the Shimura variety $Sh_K(G, X)$ parametrize a family of motives; unlike in abelian type (moduli of abelian varieties, etc.), in non-abelian type this problem remains completely mysterious. I will discuss joint work with Christian Klevdal showing that for "superrigid," including all non-abelian type, Shimura varieties the points (over number fields, say) at least yield compatible systems of l-adic representations, which should be the l-adic realizations of the conjectural motives. Time permitting, I will discuss some work in progress (with Jake Huryn, Kiran Kedlaya, and Klevdal) on a crystalline analogue.
number theory
Audience: researchers in the discipline
( paper )
| Organizers: | Sol Friedberg*, Benjamin Howard, Dubi Kelmer, Spencer Leslie, Keerthi Madapusi Pera, Bjorn Poonen*, Andrew Sutherland*, Wei Zhang* |
| *contact for this listing |