Let 𝕍{{\mathbb{V}}} be a polarized variation of integral Hodge structure on a smooth complex quasi-projective variety S . In this paper, we show that the union of the non-factor special subvarieties for (S,𝕍){(S,{\mathbb{V}})}, which are of Shimura type with dominant period maps, is a finite union of special subvarieties of S . This generalizes previous results of Clozel and Ullmo (2005) and Ullmo (2007) on the distribution of the non-factor (in particular, strongly) special subvarieties in a Shimura variety to the non-classical setting and also answers positively the geometric part of a conjecture of Klingler on the André–Oort conjecture for variations of Hodge structures.

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关于霍奇结构变化的几何安德烈-奥尔特猜想

令 𝕍{{\mathbb{V}}} 是光滑复拟射影变体 S 上积分霍奇结构的极化变体。在本文中，我们证明 (S,𝕍){(S,{\mathbb{V}})} 的非因子特殊子变体的并集是具有主导周期映射的 Shimura 类型，是一个有限并集S 的特殊子变体。这将 Clozel 和 Ullmo (2005) 以及 Ullmo (2007) 先前关于 Shimura 变种中非因子（特别是强）特殊子变体分布的结果推广到非经典环境中，并且正面回答了克林勒对霍奇结构变化的安德烈-奥尔特猜想的猜想。