Proposition 4.2. Assuming that:

• we define

  $$\begin{array}{llll}\hfill \psi :E& \to {\mathrm{Pic}}^0(E)& \hfill & \\ \hfill P& \mapsto [(P)-(0_E)]& \hfill & \end{array}$$

• (i) $\psi (P\oplus Q)=\psi (P)+\psi (Q)$.
• (ii) $\psi$ is a bijection.