MIXED HODGE STRUCTURES WITH MODULUS

Florian Ivorra; Takao Yamazaki

doi:10.1017/S1474748020000043

MIXED HODGE STRUCTURES WITH MODULUS

Florian Ivorra, Takao Yamazaki

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	161-195
Number of pages	35
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	21
Issue number	1
DOIs	https://doi.org/10.1017/S1474748020000043
Publication status	Published - 2022 Jan 2

Keywords

Enriched Hodge structure
Formal Hodge structure
Laumon 1-motives

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1017/S1474748020000043

Cite this

@article{081f5cc2f5cf407488d0b0435b026d16,

title = "MIXED HODGE STRUCTURES WITH MODULUS",

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 structure, Formal Hodge structure, Laumon 1-motives",

author = "Florian Ivorra and Takao Yamazaki",

note = "Funding Information: Part of this work was done during a visit of the first author at the Tohoku University and a visit of the second author at the University of Rennes 1. The hospitality of those institutions is gratefully appreciated. This work is supported by JSPS KAKENHI Grant (15K04773) and the University of Rennes 1. We would like to thank the referee for careful reading and detailed comments. Publisher Copyright: {\textcopyright} 2020 Cambridge University Press.",

year = "2022",

month = jan,

day = "2",

doi = "10.1017/S1474748020000043",

language = "English",

volume = "21",

pages = "161--195",

journal = "Journal of the Institute of Mathematics of Jussieu",

issn = "1474-7480",

publisher = "Cambridge University Press",

number = "1",

}

TY - JOUR

T1 - MIXED HODGE STRUCTURES WITH MODULUS

AU - Ivorra, Florian

AU - Yamazaki, Takao

N1 - Funding Information: Part of this work was done during a visit of the first author at the Tohoku University and a visit of the second author at the University of Rennes 1. The hospitality of those institutions is gratefully appreciated. This work is supported by JSPS KAKENHI Grant (15K04773) and the University of Rennes 1. We would like to thank the referee for careful reading and detailed comments. Publisher Copyright: © 2020 Cambridge University Press.

PY - 2022/1/2

Y1 - 2022/1/2

N2 - 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.

AB - 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.

KW - Enriched Hodge structure

KW - Formal Hodge structure

KW - Laumon 1-motives

UR - http://www.scopus.com/inward/record.url?scp=85081553345&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85081553345&partnerID=8YFLogxK

U2 - 10.1017/S1474748020000043

DO - 10.1017/S1474748020000043

M3 - Article

AN - SCOPUS:85081553345

SN - 1474-7480

VL - 21

SP - 161

EP - 195

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

IS - 1

ER -

MIXED HODGE STRUCTURES WITH MODULUS

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this