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

Bidragets oversatte titel: A logarithmic interpretation of Edixhoven's jumps for Jacobians

Dennis Eriksson, Lars Halvard Halle, Johannes Nicaise

Institut for Matematiske Fag

4 Citationer (Scopus)

Abstract

Let $A$ be an abelian variety over a discretely valued field. Edixhoven has defined a filtration on the special fiber of the N\'eron model of $A$ that measures the behaviour of the N\'eron 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 $C$.

Bidragets oversatte titel	A logarithmic interpretation of Edixhoven's jumps for Jacobians
Originalsprog	Engelsk
Tidsskrift	Advances in Mathematics
Vol/bind	279
Sider (fra-til)	532–574
ISSN	0001-8708
DOI	https://doi.org/10.1016/j.aim.2015.04.007
Status	Udgivet - 6 jul. 2015

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10.1016/j.aim.2015.04.007

Citationsformater

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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

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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

Abstract

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