论文标题
与无限Oétale基本小组的品种上的积分点
Integral points on varieties with infinite étale fundamental group
论文作者
论文摘要
我们研究了与无限étale基本组品种的积分点。更准确地说，对于一个数字字段$ f $和$ x/f $是一个光滑的投射品种，我们证明，对于任何几何galois覆盖了$φ\ colon y \ colon y \至x $ to x $ tem tem tem tem tem tem tem tem the $ \ yathscr {l} $ y Mathscr {l} $ y y $ y $ y $ y $ y line $ y $ y line $ d $ d的完整$ d $ | \ Mathscr {l} | $，$ d $是几何不可约的，$ x $上的任何集合$φ（d）$都是有限的。我们将此结果应用于具有无限典型基本组的品种，以提供不可还原的新示例，以证明整体积分有限的品种。
We study integral points on varieties with infinite étale fundamental groups. More precisely, for a number field $F$ and $X/F$ a smooth projective variety, we prove that for any geometrically Galois cover $φ\colon Y \to X$ of degree at least $2\dim(X)^2$, there exists an ample line bundle $\mathscr{L}$ on $Y$ such that for a general member $D$ of the complete linear system $|\mathscr{L}|$, $D$ is geometrically irreducible and any set of $φ(D)$-integral points on $X$ is finite. We apply this result to varieties with infinite étale fundamental group to give new examples of irreducible, ample divisors on varieties for which finiteness of integral points is provable.
