This question comes from a defnition of FGA explained, the chapter of Picard scheme, wirtten by Professor Dr. Steven L. Kleiman.
Suppose $X/S$ is an abelian scheme over $S$, my question is how to define the so called $Pic^0_{X/S}$ scheme? In Kleiman's note, see https://arxiv.org/pdf/math/0504020.pdf, he defined $Pic^0_{X/S}$ to be the union of $Pic^0_{X_s/k_s}$ for any $s\in S$. However, the operation 'union' is not so clear to me. I may want to ask what is this union means? And how can we get the scheme structure by union?