COHOMOLOGICAL DEGREES AND HILBERT-FUNCTIONS OF GRADED MODULES

Making use of the recent construction of cohomological degrees functio ns, we give several estimates on the relationship between number of ge nerators and degrees of ideals and modules with applications to Hilber t functions. They extend results heretofore known from generalized Coh en-Macaulay local rings to nearly arbitrary local rings. The rules of computation these functions satisfy enables comparison with Castelnuov o-Mumford's regularity in the graded case. As application, we derive s harp improvements on predicting the outcome of effecting Noether norma lizations in tangent cones.