Arithmetic Level Raising for U(2r, 1)

Add to your list(s) Download to your calendar using vCal

• Ruiqi Bai (Cambridge)
• Tuesday 15 October 2024, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Rong Zhou.

In 1983, Ribet presented the level-raising theorem for modular forms in his ICM report. One approach to prove this is to show the surjectivity of the Abel–Jacobi map for modular curves. Recently, many high-dimensional generalizations along this approach have been established, including the works of Liu–Tian (2020), Rong Zhou (2023) on quaternionic Shimura varieties, and LTXZZ (2022), LTX (2024) on U(2r − 1, 1) Shimura varieties. In this talk, I will introduce the ongoing work with Hao Fu to show an arithmetic level- raising result for the special fiber of U(2r, 1) Shimura variety at an inert prime. Inspired by Rong’s work, we exhibit elements in the higher Chow group of the supersingular locus and use this to prove the surjectivity of the Abel–Jacobi map. A key ingredient of the proof is to show a form of Ihara’s lemma.

This talk is part of the Number Theory Seminar series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• DPMMS Lists
• DPMMS Pure Maths Seminar
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• MR13
• Number Theory Seminar
• School of Physical Sciences
• bld31

Note that ex-directory lists are not shown.