We define a notion of mixed Hodge structure with modulus that generalizes the classical notion of mixed Hodge structure introduced by Deligne and the level one Hodge structures with additive parts introduced by Kato and Russell in their description of Albanese varieties with modulus. With modulus triples of any dimension, we attach mixed Hodge structures with modulus. We combine this construction with an equivalence between the category of level one mixed Hodge structures with modulus and the category of Laumon 1-motives to generalize Kato–Russell’s Albanese varieties with modulus to 1-motives.

中文翻译：

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带模数的混合大杂烩结构

我们定义了一个带模量的混合 Hodge 结构的概念，它概括了 Deligne 引入的混合 Hodge 结构的经典概念，以及 Kato 和 Russell 在他们对带模量的 Albanese 品种的描述中引入的具有加法部分的一级 Hodge 结构。对于任何维度的模数三元组，我们将混合 Hodge 结构与模数结合起来。我们将这种结构与具有模量的一级混合 Hodge 结构类别和 Laumon 1-动机类别之间的等价性结合起来，以将加藤-罗素的带模量的 Albanese 变体推广到 1-动机。