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Let $k$ be an algebraically closed field of positive characteristic. For anyinteger $m \geq 2$, we show that the Hodge numbers of a smooth projective$k$-variety can take on any combination of values modulo $m$, subject only toSerre duality. In particular, there are no non-trivial polynomial relationsbetween the Hodge numbers.

The construction problem for Hodge numbers modulo an integer in positive characteristic