Compatibility of the canonical l-adic local systems on exceptional Shimura varieties

Let G, X be a Shimura datum, and let K be a compact open subgroup of G(Af). One hopes that under mild assumptions on G and K, the points of the Shimura variety ShK(G, X) parametrize a family of motives; in abelian type this is well-understood, but in non-abelian type it is completely mysterious. I will discuss joint work with Christian Klevdal showing that for exceptional 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.

For more info, see https://ashvin-swaminathan.github.io/home/NTSeminar.html