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The Cherlin-Zilber conjecture says that if $ G $ is a simple group of finite Morley rank, then $ G $ is isomorphic to an algebraic group over an algebraically closed field. (Here, "simple" is meant in the group-theoretic sense, not the model-theoretic sense.) The Cherlin-Zilber conjecture is essentially the last vestige of Zilber's principle that might really be true.