Regular Decomposition of Ordinarity in Generic Exponential Sums

Abstract

In papers published in 1993 and 2004 Wan establishes a decomposition theory for the generic Newton polygon associated to a family of $L$-functions of $n$-dimensional exponential sums over finite fields. In this work we generalize the star, parallel hyperplane and collapsing decomposition, demonstrating that each is a generalization of a complete regular decomposition.