Saturation and Castelnuovo–Mumford regularity

Let I be a homogeneous ideal of the polynomial ring K[x0,…,xn], where K is an arbitrary field. Avoiding the construction of a minimal graded free resolution of I, we provide effective methods for computing the Castelnuovo–Mumford regularity of I that also compute other cohomological invariants of K[x0,…,xn]/I.