Analytic Spread and Associated primes of divisorial filtrations

We prove that a classical theorem of McAdam about the analytic spread of an ideal in a Noetherian local ring is true for divisorial filtrations on an excellent local ring $R$ which is either of equicharacteristic zero or of dimension $\le 3$. In fact, the proof is valid whenever resolution of singularities holds.Comment: 12 pages. In this version the assumption of being normal is removed from the results of the paper, Theorems 1.3 and 1.4. The theorems are extended to hold for Q-divisorial filtrations. arXiv admin note: text overlap with arXiv:2203.0593