= Poincaré line bundle
{c}
{title2=$P_A\text{ on }A\times\widehat A$}
The normalized universal <line bundle> restricts to the class $\xi$ on $A\times\{\xi\}$ and is trivialized on both zero sections. For a <line bundle> $L$ on an <abelian variety>, its <homomorphism associated to a line bundle on an abelian variety> satisfies
$$
(\operatorname{id},\phi_L)^*P_A\cong m^*L\otimes p_1^*L^{-1}\otimes p_2^*L^{-1}
$$
as <Picard group> classes. A choice of trivialization of $L_0$ normalizes the right side; uniqueness then follows from the <Seesaw theorem>.
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