Slope estimates of Artin-Schreier curves
| dc.creator | Scholten, Jasper | |
| dc.creator | Zhu, Hui June | |
| dc.date | 2001-05-01 | |
| dc.date.accessioned | 2026-07-07T04:41:33Z | |
| dc.date.available | 2026-07-07T04:41:33Z | |
| dc.description | Let f(x) = x^d + a_{d-1}x^{d-1} + ... + a_0 be a polynomial of degree d in Q[x]. For every prime number p coprime to d and f(x) in (Z_p \cap Q)[x], let X/F_p be the Artin-Schreier curve defined by the affine equation y^p - y = f(x) mod p. Let NP_1(X/F_p) be the first slope of the Newton polygon of X/F_p. We prove that there is a Zariski dense subset U in the space A^d of degree-d monic polynomials over Q such that for all f(x) in U, the limit of NP_1(X/F_p) is equal to 1/d as p goes to infinity. This is a ``first slope version'' of a conjecture of Wan. Let X/F_pbar be an Artin-Schreier curve defined by the affine equation y^p - y = F(x) where F(x) = x^d + A_{d-1}x^{d-1} + ... + A_0. We prove that if p>d>1 then NP_1(X/F_pbar) >= ceiling((p-1)/d)/(p-1). If p>2d>3, we give a sufficient condition for the equality to hold. | |
| dc.description | 20 pages, Latex | |
| dc.identifier | https://arxiv.org/abs/math/0105005 | |
| dc.identifier | http://arxiv.org/abs/math/0105005 | |
| dc.identifier | Compositio Math. 137 (2003), 275-292. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61402 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.title | Slope estimates of Artin-Schreier curves | |
| dc.type | text |