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SUMMARY:Yujie Xu (MIT)
DTSTART:20221004T203000Z
DTEND:20221004T213000Z
DTSTAMP:20260423T130410Z
UID:MITNT/56
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/56/">N
 ormalization in the integral models of Shimura varieties of abelian type</
 a>\nby Yujie Xu (MIT) as part of MIT number theory seminar\n\nLecture held
  in Room 2-143 in the Simons Building (building 2).\n\nAbstract\nShimura v
 arieties are moduli spaces of abelian varieties with extra structures. Man
 y interesting questions about abelian varieties have been answered by stud
 ying the geometry of Shimura varieties. \n\nIn order to study the mod $p$ 
 points of Shimura varieties\, over the decades\, various mathematicians (e
 .g. Rapoport\, Kottwitz\, etc.) have constructed nice integral models of S
 himura varieties. \nIn this talk\, I will discuss some motivic aspects of 
 integral models of Hodge type (or more generally abelian type) constructed
  by Kisin and Kisin-Pappas. I will talk about my recent work on removing t
 he normalization step in the construction of such integral models\, which 
 gives closed embeddings of Hodge type integral models into Siegel integral
  models. I will also mention an application to toroidal compactifications 
 of such integral models. Such results (and their proof techniques) have fo
 und interesting applications to the Kudla program (and various other progr
 ams!).\n\nIf time permits\, I will also mention a new result on connected 
 components of affine Deligne–Lusztig varieties\, which gives us a new CM
  lifting result for integral models of Shimura varieties at parahoric leve
 ls and serves as an ingredient for my main theorem at parahoric levels.\n
LOCATION:https://researchseminars.org/talk/MITNT/56/
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