The Largest Non-vanishing Degree of Graded Local Cohomology Modules

This paper gives characterizations for the largest non-vanishing degree of the local cohomology modules of a graded ringSin terms of a reduction ofS + and of the associated graded ring of an idealIin terms of any reduction ofI. As a consequence, this invariant can be computed explicitly for the associated graded ring of any ideal generated by ad-sequence and of ideals having small analytic deviation.