Motivic zeta functions of abelian varieties, and the monodromy conjecture

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Motivic zeta functions of abelian varieties, and the monodromy conjecture. / Halle, Lars Halvard; Nicaise, Johannes.

I: Advances in Mathematics, Bind 227, Nr. 1, 01.05.2011, s. 610-653.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Halle, LH & Nicaise, J 2011, 'Motivic zeta functions of abelian varieties, and the monodromy conjecture', Advances in Mathematics, bind 227, nr. 1, s. 610-653. https://doi.org/10.1016/j.aim.2011.02.011

APA

Halle, L. H., & Nicaise, J. (2011). Motivic zeta functions of abelian varieties, and the monodromy conjecture. Advances in Mathematics, 227(1), 610-653. https://doi.org/10.1016/j.aim.2011.02.011

Vancouver

Halle LH, Nicaise J. Motivic zeta functions of abelian varieties, and the monodromy conjecture. Advances in Mathematics. 2011 maj 1;227(1):610-653. https://doi.org/10.1016/j.aim.2011.02.011

Author

Halle, Lars Halvard ; Nicaise, Johannes. / Motivic zeta functions of abelian varieties, and the monodromy conjecture. I: Advances in Mathematics. 2011 ; Bind 227, Nr. 1. s. 610-653.

Bibtex

@article{c37c983cd3c24cde8210909773dbd0cd,
title = "Motivic zeta functions of abelian varieties, and the monodromy conjecture",
abstract = "We prove for abelian varieties a global form of Denef and Loeser's motivic monodromy conjecture, in arbitrary characteristic. More precisely, we prove that for every tamely ramified abelian variety A over a complete discretely valued field with algebraically closed residue field, its motivic zeta function has a unique pole at Chai's base change conductor c(A) of A, and that the order of this pole equals one plus the potential toric rank of A. Moreover, we show that for every embedding of Ql in C, the value exp(2πic(A)) is an l-adic tame monodromy eigenvalue of A. The main tool in the paper is Edixhoven's filtration on the special fiber of the N{\'e}ron model of A, which measures the behavior of the N{\'e}ron model under tame base change.",
keywords = "Abelian varieties, Monodromy conjecture, Motivic zeta functions, N{\'e}ron models",
author = "Halle, {Lars Halvard} and Johannes Nicaise",
year = "2011",
month = may,
day = "1",
doi = "10.1016/j.aim.2011.02.011",
language = "English",
volume = "227",
pages = "610--653",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press",
number = "1",

}

RIS

TY - JOUR

T1 - Motivic zeta functions of abelian varieties, and the monodromy conjecture

AU - Halle, Lars Halvard

AU - Nicaise, Johannes

PY - 2011/5/1

Y1 - 2011/5/1

N2 - We prove for abelian varieties a global form of Denef and Loeser's motivic monodromy conjecture, in arbitrary characteristic. More precisely, we prove that for every tamely ramified abelian variety A over a complete discretely valued field with algebraically closed residue field, its motivic zeta function has a unique pole at Chai's base change conductor c(A) of A, and that the order of this pole equals one plus the potential toric rank of A. Moreover, we show that for every embedding of Ql in C, the value exp(2πic(A)) is an l-adic tame monodromy eigenvalue of A. The main tool in the paper is Edixhoven's filtration on the special fiber of the Néron model of A, which measures the behavior of the Néron model under tame base change.

AB - We prove for abelian varieties a global form of Denef and Loeser's motivic monodromy conjecture, in arbitrary characteristic. More precisely, we prove that for every tamely ramified abelian variety A over a complete discretely valued field with algebraically closed residue field, its motivic zeta function has a unique pole at Chai's base change conductor c(A) of A, and that the order of this pole equals one plus the potential toric rank of A. Moreover, we show that for every embedding of Ql in C, the value exp(2πic(A)) is an l-adic tame monodromy eigenvalue of A. The main tool in the paper is Edixhoven's filtration on the special fiber of the Néron model of A, which measures the behavior of the Néron model under tame base change.

KW - Abelian varieties

KW - Monodromy conjecture

KW - Motivic zeta functions

KW - Néron models

UR - http://www.scopus.com/inward/record.url?scp=79952706904&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2011.02.011

DO - 10.1016/j.aim.2011.02.011

M3 - Journal article

AN - SCOPUS:79952706904

VL - 227

SP - 610

EP - 653

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 1

ER -

ID: 233909786