Newton stratification for polynomials: the open stratum

2006/03/11 by Blache, Régis, Férard, Eric
#11L03 #11T23 #14G15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.math/0603264

Abstract

In this paper we consider the Newton polygons of L-functions coming from additive exponential sums associated to a polynomial over a finite field \F_q. These polygons define a stratification of the space of polynomials of fixed degree. We determine the open stratum: we give the generic Newton polygon for polynomials of degree d≥ 2 when the characteristic p is greater than 3d, and the Hasse polynomial, i.e. the equation defining the hypersurface complementary to the open stratum.

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