Explicit Construction of Self-Dual Integral Normal Bases for the Square-Root of the Inverse Different - Mathematics > Number TheoryReportar como inadecuado




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/







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