标题： Hodge理论在亚历山大模上的相容性 显示英文标题

标题： Compatibility of Hodge Theory on Alexander Modules

摘要： 设$U$为一个光滑连通的复代数簇，令$f\colon U\to \mathbb C^*$为一个代数映射。 对于对$(U,f)$可以关联一个无限循环覆盖$U^f$，并且（同调）亚历山大模被定义为该覆盖的同调群。 在两项最近的研究中，其中一项是与 Geske、Maxim 和 Wang 合作的，我们开发了两种不同的方法来在亚历山大模上赋予混合霍奇结构。 由于它们通常不是有限维的，每种方法都将亚历山大模替换为不同的有限维模：一种方法取其挠子模，另一种方法取有限维商模，且这些构造不能直接比较。 在本文中，我们证明这两种构造是相容的，即从挠子模到商模的映射是一个混合霍奇结构同态。 显示英文摘要

摘要： Let $U$ be a smooth connected complex algebraic variety, and let $f\colon U\to \mathbb C^*$ be an algebraic map. To the pair $(U,f)$ one can associate an infinite cyclic cover $U^f$, and (homology) Alexander modules are defined as the homology groups of this cover. In two recent works, the first of which is joint with Geske, Maxim and Wang, we developed two different ways to put a mixed Hodge structure on Alexander modules. Since they are not finite dimensional in general, each approach replaces the Alexander module by a different finite dimensional module: one of them takes the torsion submodule, the other takes finite dimensional quotients, and the constructions are not directly comparable. In this note, we show that both constructions are compatible, in the sense that the map from the torsion to the quotients is a mixed Hodge structure morphism.