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We show that the reduction to positive characteristic of the multiplier ideal in the sense of de Fernex and Hacon agrees with the test ideal for infinitely many primes, assuming that the variety is numerically   Q  ‐Gorenstein. It follows, in particular, that this reduction property holds in dimension 2 for all normal surfaces.

Comparing multiplier ideals to test ideals on numerically ℚ‐Gorenstein varieties