Newton slopes for Artin-Schreier-Witt towers
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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.
Original language | English |
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Journal | Mathematische Annalen |
Volume | 364 |
Issue number | 3 |
Pages (from-to) | 1451-1468 |
ISSN | 0025-5831 |
DOIs | |
Publication status | Published - 2016 |
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