Identity component of the Picard group
= Identity component of the Picard group
{c}
{title2=$\operatorname{Pic}^0X$}
{wiki=Picard_group#Picard_scheme}
For an abelian variety,
$$
\operatorname{Pic}^0X=\{L\in\operatorname{Pic}X:\phi_L=0\}
$$
is the subgroup of translation-invariant line bundles.