Let $X$ be a quasi-projective variety over a number field, admitting (after passage to $\mathbb {C}$) a geometric variation of Hodge structure whose period mapping has zero-dimensional fibers. Then the integral points of $X$ are sparse: the number of such points of height $\leq B$ grows slower than any positive power of $B$. For example, homogeneous integral polynomials in a fixed number of variables and degree, with discriminant divisible only by a fixed set of primes, are sparse when considered up to integral linear substitutions.

中文翻译：

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品种模空间上积分点的稀疏性

令 $X$ 是一个数域上的拟射变簇，承认（在通过 $\mathbb {C}$ 之后）Hodge 结构的几何变化，其周期映射具有零维纤维。则 $X$ 的积分点是稀疏的：高度为 $\leq B$ 的点的数量比 $B$ 的任何正幂增长得慢。例如，具有固定数量的变量和次数的齐次积分多项式（判别式只能被一组固定的素数整除）在考虑到积分线性替换时是稀疏的。