Cohomology of induced modules in rings of differential operators
Abstract
Let K be a field of characteristic zero and let Δ ={δ 1 ,…,δ n } be a set of commuting K -derivations of the commutative Noetherian K -algebra R . Let S = R [ X 1 ,…, X n ] be the corresponding ring of differential operators, so [ X i , r ] = X i r − r X i =δ i ( r and [ X i , X j ]=0, for 1≦ i , j ≦ n . Let M be a maximal ideal of R with R / M of finite dimension over K . The purpose of this note is to describe the groups