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
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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