On Weil Numbers in Cyclotomic Fields

Abstract

In this note, we investigate the p-adic behavior of Weil numbers in the cyclotomic $\mathbb{Z}\_p$-extension of $\mathbb{Q}(\zeta \_p).$ We determlne the characteristic ideal of the quotient of semi-local units by Weil numbers in terms of the characteristic ideals of some classical modules that appear in Iwasawa Theory.