  We study the algebraic Gauss-Manin system and the algebraic Brieskorn module
associated to a polynomial mapping with isolated singularities. Since the
algebraic Gauss-Manin system does not contain any information on the cohomology
of singular fibers, we first construct a non quasi-coherent sheaf which gives
the cohomology of every fiber. Then we study the algebraic Brieskorn module,
and show that its position in the the algebraic Gauss-Manin system is
determined by a natural map to quotients of local analytic Gauss-Manin systems,
and its pole part by the vanishing cycles at infinity, comparing it with the
Deligne extension. This implies for example a formula for the determinant of
periods. In the two-dimensional case we can describe the global structure of
the algebraic Gauss-Manin system rather explicitly.
