Related papers: Abelian $p$-extensions and additive polynomials

We determine the distribution of discriminants of wildly ramified elementary-abelian extensions of local and global function fields in characteristic $p$. For local and rational function fields, we also give precise formulae for the number…

Abelian groups are classified by the existence of certain additive decompositions of group-valued functions of several variables with arity gap 2.

In this paper we find the genus field of finite abelian extensions of the global rational function field. We introduce the term conductor of constants for these extensions and determine it in terms of other invariants. We study the…

We study the arithmetic aspects of the finite group of extensions of abelian varieties defined over a number field. In particular, we establish relations with special values of L-functions and congruences between modular forms.

Algebraic methods are used to construct families of unramified abelian extensions of some families of number fields with specified Galois groups.

Let $G\subset x{\mathbb F}_q[\![x]\!]$ ($q$ is a power of the prime $p$) be a subset of formal power series over a finite field such that it forms a compact abelian $p$-adic Lie group of dimension $d\ge 1$. We establish a necessary and…

We study on finite unramified extensions of global function fields (function fields of one valuable over a finite field). We show two results. One is an extension of Perret's result about the ideal class group problem. Another is a…

We define a variant of normal basis, called a {\em Galois scaffolding}, that allows for an easy determination of valuation, and has implications for Galois module structure. We identify fully ramified, elementary abelian extensions of local…

We give a brief re-exposition of the theory due to Pauli and Sinclair of ramification polygons of Eisenstein polynomials over p-adic fields, their associated residual polynomials and an algorithm to produce all extensions for a given…

Let $G$ be a finite abelian $p$-group. We count \'etale $G$-extensions of global rational function fields $\mathbb F_q(T)$ of characteristic $p$ by the degree of what we call their Artin-Schreier conductor. The corresponding (ordinary)…

In this paper we obtain the extended genus field of a finite abelian extension of a global rational function field. We first study the case of a cyclic extension of prime power degree. Next, we use that the extended genus fields of a…

For the ring R of integers of a ramified extension of the field of p-adic numbers and a cyclic group G of prime order p we study the extensions of the additive groups of R-representations modules of G by the group G.

In the present work, we determine explicitly the genus of any separable cubic extension of any global function field given the minimal polynomial of the extension. We give algorithms computing the ramification data and the genus of any…

In this paper some classes of local polynomial functions on abelian groups are characterized by the properties of their variety. For this characterization we introduce a numerical quantity depending on the variety of the local polynomial…

The article at hand contains exact asymptotic formulas for the distribution of conductors of abelian p-extensions of global function fields of characteristic p. These yield a new conjecture for the distribution of discriminants fueled by an…

We define abelian extensions of algebras in congruence-modular varieties. The theory is sufficiently general that it includes, in a natural way, extensions of R-modules for a ring R. We also define a cohomology theory, which we call clone…

In this paper we present a classification of the possible upper ramification jumps for an elementary abelian p-extension of a p-adic field. The fundamental step for the proof of the main result is the computation of the ramification…

We give a characterization of ramification groups of local fields with imperfect residue fields, using those for local fields with perfect residue fields. As an application, we reprove an equality of ramification groups for abelian…

We develop the theory of Abelian functions associated with algebraic curves. The growth in computer power and an advancement of efficient symbolic computation techniques has allowed for recent progress in this area. In this paper we focus…

For any given finite abelian group, we give factorizations of the group determinant in the group algebra of any subgroup. The factorizations are an extension of Dedekind's theorem. The extension leads to a generalization of Dedekind's…