Computer Algebra
《Computer Algebra》 · 第 25–26 页 · Section 5「The theorem of the cube」,Theorem 5.16 and Corollary 5.18
The seesaw principle. […] Let $\mathcal L$ and $\mathcal M$ be invertible sheaves on $V\times T$, with $V$ complete. If $\mathcal L_t\simeq\mathcal M_t$ for all $t\in T$, then $\mathcal L\simeq\mathcal M\otimes q^*\mathcal N$ for some invertible sheaf $\mathcal N$ on $T$; if in addition $\mathcal L_v\simeq\mathcal M_v$ for at least one $v\in V(k)$, then $\mathcal L\simeq\mathcal M$.