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We prove vanishing theorems of cohomology groups of local system, which generalize Kita and Noumi's result and partially Aomoto's result. Main ingredients of our proof are the Hodge to de Rham spectral sequence and Serre's vanishing theorem in algebraic geometry.doi:10.1017/s0027763000006310 fatcat:sagvcgtmyzggpgfoddlzlulrke