Reference request: Sheaf for the Zariski topology In my course notes page 62 I've read the following: let $(E,0)$ be an elliptic curve over an arbitrary scheme $S$, then $U\rightarrow\ker(\,0^*_U:\operatorname{Pic}(E_U)\rightarrow \operatorname{Pic}(U))$ is a sheaf for the Zariski topology.
What is "sheaf for the Zariski topology" ? So far I know what is a sheaf and what is Zariski topology. I'll be thankful for any references in this subject.

Quite simply, a sheaf is defined on open sets and the Zariski topology is a choice of open sets. So a "sheaf for the Zariski topology" is an assignment of groups/modules/rings etc. (Picard groups in your case) to Zariski-open sets of the top space in a way that compatible sections glue uniquely.
