On the vanishing of local cohomology in characteristic p > 0

Abstract

Let R be a d -dimensional regular local ring of characteristic p > 0 with maximal ideal $\mathfrak m$ , let I be an ideal of R and let A = R / I . We describe some properties of the local cohomology module H i I ( R ), in particular its vanishing, in terms of the Frobenius action on the local cohomology module $H^{d-i}_{\mathfrak m}(A)$ .