Let $G$ be an algebraic group defined over an (algebraically closed) field $k$. Then one can obtain a formal group law by completing the multiplication map $m: G \times G \to G$ at the unit of $G$.

The formal group law of $\mathbb{G}_a$ thus obtained will be given by the series $F(x,y)=x+y$ (up to isomorphism of formal group laws), as one can easily see.

In characteristic 0, over $\mathbb{C}$ at least, Abelian varietes are just quotients of finite products $\mathbb{G}_a$ by a lattice, so they have the same formal group law.

What can one say about the formal group laws of Abelian varieties (generally understood as projective algebraic groups) over fields other than $\mathbb C$? How can one see that it is isomorphic to $F(x,y)=x+y$ (or $n$-dimensional versien thereof)? What is it in characteric $p$?

Let $G$ be an algebraic group defined over an (algebraically closed) field $k$. Then one can obtain a formal group law by completing the multiplication map $m: G \times G \to G$ at the unit of $G$.

The formal group law of $\mathbb{G}_a$ thus obtained will be given by the series $F(x,y)=x+y$ (up to isomorphism of formal group laws), as one can easily see.

In characteristic 0, over $\mathbb{C}$ at least, Abelian varietes are just quotients of finite products $\mathbb{G}_a$ by a lattice, so they have the same formal group law.

What can one say about the formal group laws of Abelian varieties (now understood as just projective algebraic groups) over fields other than $\mathbb C$? How can one see that it is isomorphic to $F(x,y)=x+y$ (or $n$-dimensional versien thereof)? What is it in characteric $p$?