= Solution
A <presheaf> $F:\mathsf{Sch}^{\mathrm{op}}\to\mathsf{Set}$ is a <Zariski sheaf> when every <Zariski cover> $(U_i\to T)$ gives an <equalizer> diagram
$$
\boxed{F(T)\longrightarrow\prod_iF(U_i)\rightrightarrows\prod_{i,j}F(U_i\times_TU_j).}
$$
Thus compatible local elements glue to a unique element of $F(T)$. Compatibility means that the two restrictions agree on every intersection. This includes the empty <Zariski cover> of the empty <scheme>, so $F(\varnothing)$ is a singleton.
Back to article page
