The multiplier ideal is a universal test ideal

this paper establishes, roughly speaking, that the test ideal and the multiplier ideal are indeed equal for every normal local Q-Gorenstein ring essentially of finite type over a field of characteristic zero. Actually, the meaning of the test ideal in characteristic zero is somewhat ambiguous, but the work here shows that for normal local Q-Gorenstein rings of characteristic zero, the multiplier ideal acts as a universal test ideal--- after reducing mod p we get the test ideal in each characteristic p model. In particular, this shows that a universal test ideal Key words and phrases. Multiplier ideal, test ideal, tight closure, F-regular, log-terminal.