Lemma of the day

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Let X be a quasi-separated algebraic space. Let E be an object of DQCoh(OX). Let a ≤ b. The following are equivalent

  1. E has tor amplitude in [a,b], and
  2. for all F in QCoh(OX) we have Hi(E ⊗L F)=0 for i not in [a,b].

See Tag 08IL.