abelian subvariety

《Computer Algebra》 · 第 42 页 · Section 10「The complete reducibility theorem」，Proposition 10.1

Let $B$ be an abelian subvariety of an abelian variety $A$. There exists an abelian subvariety $B'$ of $A$ such that the map $B\times B'\to A$, $(b,b')\mapsto b+b'$, is an isogeny.