On some local cohomology invariants of local rings
  Let A be a commutative Noetherian local ring containing a field of characteristic p>0. The integer invariants $\lambda_{i,j}(A)$ have been introduced in an old paper of ours. In this paper we completely describe $\lambda_{d,d}(A)$, where d=dimA, in terms of the topology of SpecA. 
Gennady Lyubeznik