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.

You can define a sheaf $\cal F$ with values in a category $\mathbf{C}$ on any topological space $X$ by letting ${\cal F}(U)$ be an object in $\mathbf{C}$ for any open set $U\subset X$ so that the usual axioms are met.
E.g. see this Wikipedia entry.
To fix ideas you may think that $\mathbf{C}$ is the category of groups, so that ${\cal F}(U)$ is a group for every open $U\subset X$ and the restriction maps
$$
\rho_{U,V}:{\cal F}(V)\longrightarrow{\cal F}(U)
$$
will be homomorphisms for every inclusion $U\subset V$ of open sets.
