On certain rings of differentiable type and finiteness properties of local cohomology (Q376012)

Let \(R\) be a regular ring and \(I\) an ideal of \(R\). In 1993, Lyubeznik conjectured that each local cohomology module \(H_I^i(R)\) has finitely many associated prime ideals. In the paper under review, it is shown that if \(R\) is local of mixed characteristic \(p>0,\) then the set of associated primes of \(H_I^i(R)\) that do not contain \(p\) is finite for all \(i\geq 0\). The proof involves a large amount of the theory of \(D\)-modules.