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SUMMARY:Stefan Patrikis (Ohio State University)
DTSTART:20241203T200000Z
DTEND:20241203T210000Z
DTSTAMP:20260419T152110Z
UID:BC-MIT/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BC-MIT/15/">
 Compatibility of canonical l-adic local systems on Shimura varieties of no
 n-abelian type</a>\nby Stefan Patrikis (Ohio State University) as part of 
 BC-MIT number theory seminar\n\nLecture held in Maloney 560 at Boston Coll
 ege.\n\nAbstract\nLet $(G\, X)$ be a Shimura datum\, and let $K$ be a comp
 act open subgroup of $G(\\mathbb{A}_f)$. One hopes that under mild assumpt
 ions on $G$ and $K$\, the points of the Shimura variety $Sh_K(G\, X)$ para
 metrize a family of motives\; unlike in abelian type (moduli of abelian va
 rieties\, etc.)\, in non-abelian type this problem remains completely myst
 erious. I will discuss joint work with Christian Klevdal showing that for 
 "superrigid\," including all non-abelian type\, Shimura varieties the poin
 ts (over number fields\, say) at least yield compatible systems of l-adic 
 representations\, which should be the l-adic realizations of the conjectur
 al motives. Time permitting\, I will discuss some work in progress (with J
 ake Huryn\, Kiran Kedlaya\, and Klevdal) on a crystalline analogue.\n
LOCATION:https://researchseminars.org/talk/BC-MIT/15/
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