  In this article we prove an arithmetic level raising theorem for the
symplectic group of degree four in the ramified case. This result is a key step
towards the Beilinson-Bloch-Kato conjecture for certain Rankin-Selberg motives
associated to orthogonal groups within the framework of the Gan-Gross-Prasad
conjecture. The theorem itself can be also viewed as an analogue of the Ihara's
lemma or the Tate conjecture for special fibers of Shimura varieties at
ramified characteristics. The proof relies heavily on the description of the
supersingular locus of certain quaternionic unitary Shimura variety which is
closely related to the classical Siegel threefold.
