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3. Problems on geometric realizations of functoriality


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      Problem 3.1.

      [Kartik Prasanna] Can one construct cycles that realize other instances of functoriality (i.e. other than Jacquet-Langlands) in special fibers of Shimura varieties? For example: the Saito-Kurokawa lifting.


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          Problem 3.2.

          [org.aimpl.user:fengt@mit.edu] Can one realize base change functoriality from Tate cycles?
            1. Remark. Treumann-Venkatesh use Smith theory to verify some version of this, with coefficients mod $p$ where $p$ is also the the degree of the base change.


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                  Problem 3.4.

                  [Yichao Tian] Can one use cycles (Hodge or Tate) to produce correspondences between eigenvarieties of different inner forms?

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