Newton stratification for polynomials: the open stratum

Details Newton stratification for polynomials: the open stratum Newton stratification for polynomials: the open stratum

2006-03-11

arxiv.org/abs/math/0603264v1

Mathematics

Algebraic Geometry

14 pages

Scientific paper

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 $d\geq 2$ 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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