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Let k be an algebraically closed field of positive characteristic. For any integer $m\ge 2$ , we show that the Hodge numbers of a smooth projective k-variety can take on any combination of values modulo m, subject only to Serre duality. In particular, there are no non-trivial polynomial relations between the Hodge numbers.doi:10.1017/fms.2020.48 fatcat:wvvxg6amibe7pkqimu4jntm6dq