= Affine lift of a holomorphic map between complex tori
{title2=$F(z)=Az+x,\quad A\Lambda_1\subseteq\Lambda_2$}
Every <holomorphic map> $V_1/\Lambda_1\to V_2/\Lambda_2$ lifts to $z\mapsto Az+x$, where $A$ is a <complex-linear map> satisfying $A\Lambda_1\subseteq\Lambda_2$. Period differences of a lift lie in the discrete target <Euclidean lattice>, so its derivative is periodic. Boundedness on a compact fundamental domain and the <Liouville theorem> make this derivative constant. The linear map is unique, and the translation vector is determined modulo $\Lambda_2$.
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