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MIXED HODGE STRUCTURES WITH MODULUS

Part of: General theory of differentiable manifolds Cycles and subschemes Representation theory of rings and algebras (Co)homology theory

Published online by Cambridge University Press:  02 March 2020

Florian Ivorra Open the ORCID record for Florian Ivorra [Opens in a new window]  and
Takao Yamazaki
Florian Ivorra
Affiliation:
Institut de recherche mathématique de Rennes, UMR 6625 du CNRS, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France (florian.ivorra@univ-rennes1.fr)
Takao Yamazaki
Affiliation:
Institute of Mathematics, Tohoku University, Aoba, Sendaï, 980-8578, Japan (ytakao@math.tohoku.ac.jp)
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Abstract

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.

Keywords

enriched Hodge structureformal Hodge structureLaumon 1-motives

MSC classification

Primary: 16G20: Representations of quivers and partially ordered sets 14C30: Transcendental methods, Hodge theory , Hodge conjecture 58A14: Hodge theory
Secondary: 14F42: Motivic cohomology; motivic homotopy theory

Information

Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 1 , January 2022 , pp. 161 - 195
Copyright
© Cambridge University Press 2020

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