# Explicit Construction of Self-Dual Integral Normal Bases for the Square-Root of the Inverse Different - Mathematics > Number Theory

Explicit Construction of Self-Dual Integral Normal Bases for the Square-Root of the Inverse Different - Mathematics > Number Theory - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: Let \$K\$ be a finite extension of \$\Q p\$, let \$L-K\$ be a finite abelian Galoisextension of odd degree and let \$\bo L\$ be the valuation ring of \$L\$. We define\$A {L-K}\$ to be the unique fractional \$\bo L\$-ideal with square equal to theinverse different of \$L-K\$. For \$p\$ an odd prime and \$L-\Q p\$ contained incertain cyclotomic extensions, Erez has described integral normal bases for\$A {L-\Q p}\$ that are self-dual with respect to the trace form. Assuming\$K-\Q p\$ to be unramified we generate odd abelian weakly ramified extensions of\$K\$ using Lubin-Tate formal groups. We then use Dwork-s exponential powerseries to explicitly construct self-dual integral normal bases for thesquare-root of the inverse different in these extensions.

Autor: Erik Jarl Pickett

Fuente: https://arxiv.org/