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Let X be a curve defined over an algebraically closed field k with char(k) = p > 0. Assume that X/k is reduced. In this paper we study the unipotent part U of the Jacobian J X/k . In particular, we prove that if p is large in terms of the dimension of U , then U is isomorphic to a product of additive groups Ga.doi:10.1090/s0002-9947-00-02572-1 fatcat:47vqp3fdqnf7xhnu5fvmglu5eq