A Vanishing Theorem for Finitely Supported Ideals in Regular Local Rings

摘要

In [L5, p. 747, (b)] there is a vanishing conjecture for an ideal I in a d-dimensional regular local ring (R, m). (A stronger "CM" conjecture on that page was disproved by Hyry [Hy, p. 389, Ex. 3.6].) Suppose there is a map f: X → Spec(R) that factors as a finite sequence of blowups with smooth centers and is such that IO_X is invertible.