Character annihilator
= Character annihilator
{title2=$H^\perp$}
For a nontrivial <additive character> $\psi$ on a <local field>, the character annihilator of an additive subgroup $H$ is $H^\perp=\{y:\psi(xy)=1\text{ for all }x\in H\}$. If $\mathcal O_F^\perp=\pi^c\mathcal O_F$, then $(\pi^n\mathcal O_F)^\perp=\pi^{c-n}\mathcal O_F$. This is a character pairing construction, distinct from the <annihilator> of a module.