Product Of P-adic Symmetric Spaces

p-adic symmetric spaces play the role of complex upper half-plane in the p-adic analytic world and they are rigid spaces.In this paper we generalize a series of known results for p-adic symmetry space to the product of p-adic symmetric spaces ?_i=1^r???^di.Let ? be a torsion free and discrete subgroup of ?_i=1^r?PGL?_di+1?K?,we prove the exis-tence of covering spectral sequence for de Rham cohomology group of quotient space?\?_i=1^r???^di.Moreover if ? is cocompact,we also prove the existence of Hodge-to-de Rham spectral sequence.