Higher regulators, periods and special values of the degree four L-function of GSp(4)

We consider the degree 4 L-function associated to an automorphic representation of the symplectic group GSp(4). Starting with Beilinson's Eisenstien symbol we construct some motivic cohomology classes on the Shimura variety of GSp(4). We show that the image of these classes under the absolute Hodge regulator vanishes on the boundary of the Baily-Borel compactification of the Shimura variety. This allows to relate these classes to the product of an archimedean integral, Harris' occcult period invariant, a Deligne period and the special value of the L-function predicted by Beilinson's conjecture. The considered representation is assumed to have a Bessel model with respect to an isotropic symmetric matrix.