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.

中文翻译：

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霍奇数模正特征整数的构造问题

让ķ是具有正特征的代数闭域。对于任何整数 $m\ge 2$ ，我们证明了平滑射影的霍奇数ķ-variety 可以取任何模值组合米，仅受 Serre 对偶性约束。特别是，霍奇数之间不存在非平凡的多项式关系。