Lemma 39.9.3. Let $k$ be a field. Let $A$ be an abelian variety over $k$. For any field extension $K/k$ the base change $A_ K$ is an abelian variety over $K$.

Proof. Omitted. Note that this is why we insisted on $A$ being geometrically integral; without that condition this lemma (and many others below) would be wrong. $\square$

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).