On Iwasawa Theory over Function Fields

Details On Iwasawa Theory over Function Fields On Iwasawa Theory over Function Fields

2007-01-02

arxiv.org/abs/math/0701060v1

Mathematics

Number Theory

26 pages

Scientific paper

Let $k_{\infty}$ be a $\Z_p^d$-extension of a global function field $k$ of
characteristic $p$. Let $\Cl_{k_{\infty},p}$ be the $p$ completion of the class
group of $k_{\infty}$. We prove that the characteristic ideal of the Galois
module $\Cl_{k_{\infty},p}$ is generated by the Stickelberger element of Gross
which calculates the special values of $L$ functions.

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