The Néron component series of an abelian variety

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The Néron component series of an abelian variety. / Halle, Lars Halvard; Nicaise, Johannes.

I: Mathematische Annalen, Bind 348, Nr. 3, 08.03.2010, s. 749-778.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Halle, LH & Nicaise, J 2010, 'The Néron component series of an abelian variety', Mathematische Annalen, bind 348, nr. 3, s. 749-778. https://doi.org/10.1007/s00208-010-0495-5

APA

Halle, L. H., & Nicaise, J. (2010). The Néron component series of an abelian variety. Mathematische Annalen, 348(3), 749-778. https://doi.org/10.1007/s00208-010-0495-5

Vancouver

Halle LH, Nicaise J. The Néron component series of an abelian variety. Mathematische Annalen. 2010 mar. 8;348(3):749-778. https://doi.org/10.1007/s00208-010-0495-5

Author

Halle, Lars Halvard ; Nicaise, Johannes. / The Néron component series of an abelian variety. I: Mathematische Annalen. 2010 ; Bind 348, Nr. 3. s. 749-778.

Bibtex

@article{e65686eec8c04f8c9f3c5f29f1e185ad,
title = "The N{\'e}ron component series of an abelian variety",
abstract = "We introduce the N{\'e}ron component series of an abelian variety A over a complete discretely valued field. This is a power series in ℤ[[T]], which measures the behaviour of the number of components of the N{\'e}ron model of A under tame ramification of the base field. If A is tamely ramified, then we prove that the N{\'e}ron component series is rational. It has a pole at T = 1, whose order equals one plus the potential toric rank of A. This result is a crucial ingredient of our proof of the motivic monodromy conjecture for abelian varieties. We expect that it extends to the wildly ramified case; we prove this if A is an elliptic curve, and if A has potential purely multiplicative reduction.",
author = "Halle, {Lars Halvard} and Johannes Nicaise",
year = "2010",
month = mar,
day = "8",
doi = "10.1007/s00208-010-0495-5",
language = "English",
volume = "348",
pages = "749--778",
journal = "Mathematische Annalen",
issn = "0025-5831",
publisher = "Springer",
number = "3",

}

RIS

TY - JOUR

T1 - The Néron component series of an abelian variety

AU - Halle, Lars Halvard

AU - Nicaise, Johannes

PY - 2010/3/8

Y1 - 2010/3/8

N2 - We introduce the Néron component series of an abelian variety A over a complete discretely valued field. This is a power series in ℤ[[T]], which measures the behaviour of the number of components of the Néron model of A under tame ramification of the base field. If A is tamely ramified, then we prove that the Néron component series is rational. It has a pole at T = 1, whose order equals one plus the potential toric rank of A. This result is a crucial ingredient of our proof of the motivic monodromy conjecture for abelian varieties. We expect that it extends to the wildly ramified case; we prove this if A is an elliptic curve, and if A has potential purely multiplicative reduction.

AB - We introduce the Néron component series of an abelian variety A over a complete discretely valued field. This is a power series in ℤ[[T]], which measures the behaviour of the number of components of the Néron model of A under tame ramification of the base field. If A is tamely ramified, then we prove that the Néron component series is rational. It has a pole at T = 1, whose order equals one plus the potential toric rank of A. This result is a crucial ingredient of our proof of the motivic monodromy conjecture for abelian varieties. We expect that it extends to the wildly ramified case; we prove this if A is an elliptic curve, and if A has potential purely multiplicative reduction.

UR - http://www.scopus.com/inward/record.url?scp=77955918179&partnerID=8YFLogxK

U2 - 10.1007/s00208-010-0495-5

DO - 10.1007/s00208-010-0495-5

M3 - Journal article

AN - SCOPUS:77955918179

VL - 348

SP - 749

EP - 778

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 3

ER -

ID: 233909918