Title: Terminal 3-folds that are not Cohen-Macaulay Abstract: An important local vanishing theorem for the minimal model program is the fact that klt singularities in characteristic zero are Cohen-Macaulay. In contrast, even in the narrow setting of terminal singularities of dimension 3, we show that Cohen-Macaulayness can fail in characteristic p or mixed characteristic (0,p) for p equal to 2, 3, or 5. This is optimal, by work of Arvidsson-Bernasconi-Lacini. (These examples help to explain why the MMP remains an open question for 3-folds in characteristic 2 or 3.) The examples are quotients of regular schemes by the cyclic group G of order p. In characteristic p or mixed characteristic (0,p), such quotients can exhibit a wide range of behavior.