论文标题
Malcev完成，霍奇理论和动机
Malcev Completions, Hodge Theory, and Motives
论文作者
论文摘要
我们证明，在特征零的平稳，连接的多样性上，在所有局部系统的类别中，几何来源的局部系统在扩展下都是稳定的。因此，我们获得了Hain定理的（NORI）动机增强Malcev的单肌表示。 我们的方法是Tannakian，并依靠抽象标准来``Malcev Tolleseness''，这在本文的第一部分中得到了证明。给出了此标准的几个次要应用：d'Addezio-esnault的定理的替代证明，该证明说，Hodge Origin的本地系统在所有本地系统的类别中都稳定；上面提到的Hain定理的概括，这也肯定了Arapura的猜想。在合适的假设下，Lazda定理的替代证明给出了相对单位的DE RHAM基本组与特殊纤维的Unipitent de Rham基本组之间的同构。
We prove that, on a smooth, connected variety in characteristic zero admitting a rational point, local systems of geometric origin are stable under extension in the category of all local systems. As a consequence of this, we obtain a (Nori) motivic strengthening of Hain's theorem on Malcev completions of monodromy representations. Our methods are Tannakian, and rely on an abstract criterion for ``Malcev completeness'', which is proved in the first part of the paper. A couple of secondary applications of this criterion are given: an alternative proof of D'Addezio--Esnault's theorem, which says that local systems of Hodge origin are stable under extension in the category of all local systems; a generalisation of the theorem of Hain, mentioned above, which also affirms a conjecture of Arapura; and an alternative proof of a theorem of Lazda, which under suitable assumptions gives an isomorphism between the relative unipotent de Rham fundamental group and the unipotent de Rham fundamental group of the special fibre.
