Number Theory Seminar: Compatibility of the canonical l-adic local systems on exceptional Shimura varieties


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February 14, 2024 3:00 pm - 4:00 pm
Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138 USA

Stefan Patrikis - The Ohio State University

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.

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