How to define the pullback of a Weil divisor $D=\sum n_iY_i$? I'm particulary interested in $T^*_xD$ where $x\in X$, $X$ is an abelian variety and $T_x: X\rightarrow X$, $z\mapsto z+x$ is the translation morphism. Do we have that $Supp (T^*_xD)=SuppD-x$?
Where $SuppD-x$ is obtained by $SuppD$ after translating the points by $x$.
I hope this is true because I'm trying to understand the proof of the Theorem at page 163 from Mumford, Abelian Varieties, and if $Supp (T^*_xD)=SuppD-x$ then I understand the proof (or at least that part).
Thanks!