Iwasawa Main Conjecture for the Carlitz cyclotomic extension and applications

Autor:	Anglès, Bruno, Bandini, Andrea, Bars, Francesc, Longhi, Ignazio
Rok vydání:	2014
Předmět:	Mathematics - Number Theory Mathematics - Algebraic Geometry 11M38 11R23 11G20 14G10 11R60 11G45 11G40 14F30
Druh dokumentu:	Working Paper
Popis:	We prove an Iwasawa Main Conjecture for the class group of the $\mathfrak{p}$-cyclotomic extension $\mathcal{F}$ of the function field $\mathbb{F}_q(\theta)$ ($\mathfrak{p}$ is a prime of $\mathbb{F}_q[\theta]\,$), showing that its Fitting ideal is generated by a Stickelberger element. We use this and a link between the Stickelberger element and a $\mathfrak{p}$-adic $L$-function to prove a close analog of the Ferrero-Washington theorem for $\mathcal{F}$ and to provide informations on the $\mathfrak{p}$-adic valuations of the Bernoulli-Goss numbers $\beta(j)$ (i.e., on the values of the Goss $\zeta$-function at negative integers). Comment: Section 3 entirely rewritten
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1412.5957 Zobrazit plný text záznamu View this record from Arxiv