Newton slopes for Artin-Schreier-Witt towers

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Newton slopes for Artin-Schreier-Witt towers. / Davis, Christopher; Wan, Daqing; Xiao, Liang.

I: Mathematische Annalen, Bind 364, Nr. 3, 2016, s. 1451-1468.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Davis, C, Wan, D & Xiao, L 2016, 'Newton slopes for Artin-Schreier-Witt towers', Mathematische Annalen, bind 364, nr. 3, s. 1451-1468. https://doi.org/10.1007/s00208-015-1262-4

APA

Davis, C., Wan, D., & Xiao, L. (2016). Newton slopes for Artin-Schreier-Witt towers. Mathematische Annalen, 364(3), 1451-1468. https://doi.org/10.1007/s00208-015-1262-4

Vancouver

Davis C, Wan D, Xiao L. Newton slopes for Artin-Schreier-Witt towers. Mathematische Annalen. 2016;364(3):1451-1468. https://doi.org/10.1007/s00208-015-1262-4

Author

Davis, Christopher ; Wan, Daqing ; Xiao, Liang. / Newton slopes for Artin-Schreier-Witt towers. I: Mathematische Annalen. 2016 ; Bind 364, Nr. 3. s. 1451-1468.

Bibtex

@article{136ee8bb45ee4ad7b9cd41cbf8c0c5bc,
title = "Newton slopes for Artin-Schreier-Witt towers",
abstract = "We fix a monic polynomial f(x)∈Fq[x] over a finite field and consider the Artin-Schreier-Witt tower defined by f(x); this is a tower of curves ⋯→Cm→Cm−1→⋯→C0=A1, with total Galois group Zp. We study the Newton slopes of zeta functions of this tower of curves. This reduces to the study of the Newton slopes of L-functions associated to characters of the Galois group of this tower. We prove that, when the conductor of the character is large enough, the Newton slopes of the L-function form arithmetic progressions which are independent of the conductor of the character. As a corollary, we obtain a result on the behavior of the slopes of the eigencurve associated to the Artin-Schreier-Witt tower, analogous to the result of Buzzard and Kilford.",
author = "Christopher Davis and Daqing Wan and Liang Xiao",
year = "2016",
doi = "10.1007/s00208-015-1262-4",
language = "English",
volume = "364",
pages = "1451--1468",
journal = "Mathematische Annalen",
issn = "0025-5831",
publisher = "Springer",
number = "3",

}

RIS

TY - JOUR

T1 - Newton slopes for Artin-Schreier-Witt towers

AU - Davis, Christopher

AU - Wan, Daqing

AU - Xiao, Liang

PY - 2016

Y1 - 2016

N2 - We fix a monic polynomial f(x)∈Fq[x] over a finite field and consider the Artin-Schreier-Witt tower defined by f(x); this is a tower of curves ⋯→Cm→Cm−1→⋯→C0=A1, with total Galois group Zp. We study the Newton slopes of zeta functions of this tower of curves. This reduces to the study of the Newton slopes of L-functions associated to characters of the Galois group of this tower. We prove that, when the conductor of the character is large enough, the Newton slopes of the L-function form arithmetic progressions which are independent of the conductor of the character. As a corollary, we obtain a result on the behavior of the slopes of the eigencurve associated to the Artin-Schreier-Witt tower, analogous to the result of Buzzard and Kilford.

AB - We fix a monic polynomial f(x)∈Fq[x] over a finite field and consider the Artin-Schreier-Witt tower defined by f(x); this is a tower of curves ⋯→Cm→Cm−1→⋯→C0=A1, with total Galois group Zp. We study the Newton slopes of zeta functions of this tower of curves. This reduces to the study of the Newton slopes of L-functions associated to characters of the Galois group of this tower. We prove that, when the conductor of the character is large enough, the Newton slopes of the L-function form arithmetic progressions which are independent of the conductor of the character. As a corollary, we obtain a result on the behavior of the slopes of the eigencurve associated to the Artin-Schreier-Witt tower, analogous to the result of Buzzard and Kilford.

U2 - 10.1007/s00208-015-1262-4

DO - 10.1007/s00208-015-1262-4

M3 - Journal article

VL - 364

SP - 1451

EP - 1468

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 3

ER -

ID: 64394651