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[14], we constructed l-adic representations of the Galois group Gal (F/F) whose characteristic polynomials of a Erobenius element at p coincide with the "p-th Hecke polynomials" attached to automorphic forms on B<, for almost all finite primes p of F. Such representations were obtained as l-adic analogues of the Eichler-Shimura cohomology groups, which are etale cohomology groups on Shimura curves with coefficients in certain non constant Ql-sheaves. The aim of this paper is to relate these cohomology

On the zeta function of an abelian scheme over the Shimura curve