Mixed Hodge structures with modulus
Florian Ivorra and Takao Yamazaki
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.
Reference : Journal of the Institute of Mathematics of Jussieu https://doi.org/10.1017/S1474748020000043
ArXiv link : https://arxiv.org/abs/1712.07423