On a conjecture of Wan about limiting Newton polygons

2015/10/27 by Ouyang, Yi, Yang, Jinbang
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1510.07772

Abstract

We show that for a monic polynomial f(x) over a number field K containing a global permutation polynomial of degree >1 as its composition factor, the Newton Polygon of f\mod\mathfrak p does not converge for \mathfrak p passing through all finite places of K. In the rational number field case, our result is the "only if" part of a conjecture of Wan about limiting Newton polygons.

Related

• Behaviour of Newton Polygon over polynomial composition
• A tau-conjecture for Newton polygons
• Stretching Newton polygons using pure polynomials
• On a Fiber Conjecture of Wan
• Newton Polygons of Sums on Curves II: Variation in p-adic Families