A logarithmic interpretation of Edixhoven's jumps for Jacobians

Dennis Eriksson; Lars Halvard Halle; Johannes Nicaise

doi:10.1016/j.aim.2015.04.007

A logarithmic interpretation of Edixhoven's jumps for Jacobians

Dennis Eriksson, Lars Halvard Halle, Johannes Nicaise

Department of Mathematical Sciences

4 Citations (Scopus)

Abstract

Let A be an abelian variety over a discretely valued field. Edixhoven has defined a filtration on the special fiber of the Néron model of A that measures the behavior of the Néron model under tame base change. We interpret the jumps in this filtration in terms of lattices of logarithmic differential forms in the case where A is the Jacobian of a curve C, and we give a compact explicit formula for the jumps in terms of the combinatorial reduction data of C.

Translated title of the contribution	A logarithmic interpretation of Edixhoven's jumps for Jacobians
Original language	English
Journal	Advances in Mathematics
Volume	279
Pages (from-to)	532–574
ISSN	0001-8708
DOIs	https://doi.org/10.1016/j.aim.2015.04.007
Publication status	Published - 6 Jul 2015

Keywords

math.AG

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10.1016/j.aim.2015.04.007

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title = "A logarithmic interpretation of Edixhoven's jumps for Jacobians",

abstract = "Let A be an abelian variety over a discretely valued field. Edixhoven has defined a filtration on the special fiber of the N{\'e}ron model of A that measures the behavior of the N{\'e}ron model under tame base change. We interpret the jumps in this filtration in terms of lattices of logarithmic differential forms in the case where A is the Jacobian of a curve C, and we give a compact explicit formula for the jumps in terms of the combinatorial reduction data of C.",

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T1 - A logarithmic interpretation of Edixhoven's jumps for Jacobians

AU - Eriksson, Dennis

AU - Halle, Lars Halvard

AU - Nicaise, Johannes

PY - 2015/7/6

Y1 - 2015/7/6

N2 - Let A be an abelian variety over a discretely valued field. Edixhoven has defined a filtration on the special fiber of the Néron model of A that measures the behavior of the Néron model under tame base change. We interpret the jumps in this filtration in terms of lattices of logarithmic differential forms in the case where A is the Jacobian of a curve C, and we give a compact explicit formula for the jumps in terms of the combinatorial reduction data of C.

AB - Let A be an abelian variety over a discretely valued field. Edixhoven has defined a filtration on the special fiber of the Néron model of A that measures the behavior of the Néron model under tame base change. We interpret the jumps in this filtration in terms of lattices of logarithmic differential forms in the case where A is the Jacobian of a curve C, and we give a compact explicit formula for the jumps in terms of the combinatorial reduction data of C.

KW - math.AG

U2 - 10.1016/j.aim.2015.04.007

DO - 10.1016/j.aim.2015.04.007

M3 - Journal article

SN - 0001-8708

VL - 279

SP - 532

EP - 574

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

A logarithmic interpretation of Edixhoven's jumps for Jacobians

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Keywords

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