Character idempotent
= Character idempotent
{title2=$e_\chi=|\Delta|^{-1}\sum_{\delta\in\Delta}\chi(\delta)^{-1}\delta$}
If the order of a finite abelian group $\Delta$ is invertible in the coefficient ring and all its character values belong to that ring, its character idempotents are orthogonal and sum to one. They decompose any <module> into character components. In a cyclotomic tower with odd $p$, the <Teichmüller character> provides these components integrally over $\mathbb Z_p$.