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1. Problems related to Xiao-Zhu


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      Problem 1.1.

      [Yichao Tian] Consider Xiao-Zhu specialized to Tate classes associated to Hilbert modular forms at an inert prime. In the generic case, i.e. when the Satake parameters are different, then there is a 2-dimensional space of Tate classes, and Xiao-Zhu produce a 2-dimensional space of cycles. In the nongeneric case the dimension of Tate classes is $4$, and Xiao-Zhu produce only 1 cycle. Can you find extra cycles when the Satake parameters are equal? More generally, in non-generic cases of Xiao-Zhu, can you construct the missing cycles?


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          Problem 1.2.

          [Charlotte Chan] Can the ideas of Xiao-Zhu and Liu-Tian-Xiao-Zhang-Zhu apply to “higher level” affine Deligne-Lusztig varieties or loop Deligne-Lusztig varieties?

              Cite this as: AimPL: Geometric realizations of Jacquet-Langlands correspondences, available at http://aimpl.org/geomjacqlang.