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SUMMARY:Arithmetic Level Raising for U(2r\, 1) - Ruiqi Bai (Cambridge)
DTSTART:20241015T133000Z
DTEND:20241015T143000Z
UID:TALK220372@talks.cam.ac.uk
CONTACT:Rong Zhou
DESCRIPTION:In 1983\, Ribet presented the level-raising theorem for modula
 r forms in his ICM report. One approach to prove this is to show the surje
 ctivity of the Abel–Jacobi map for modular curves. Recently\, many high-
 dimensional generalizations along this approach have been established\, in
 cluding the works of Liu–Tian (2020)\, Rong Zhou (2023) on quaternionic 
 Shimura varieties\, and LTXZZ (2022)\, LTX (2024) on U(2r − 1\, 1) Shimu
 ra varieties.\nIn this talk\, I will introduce the ongoing work with Hao F
 u to show an arithmetic level- raising result for the special fiber of U(2
 r\, 1) Shimura variety at an inert prime. Inspired by Rong’s work\, we e
 xhibit elements in the higher Chow group of the supersingular locus and us
 e this to prove the surjectivity of the Abel–Jacobi map. A key ingredien
 t of the proof is to show a form of Ihara’s lemma.
LOCATION:MR13
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