I recently began studying algebraic geometry, and in an attempt to learn about Abelian Varieties, I needed to learn the definition of a geometric vector bundle. I began reading this book, and in the notation section, it states:
By a geometric vector bundle of rank $d$ on $X$ we mean a group scheme $π: \mathbb V \to X$ over $X$ for which there exists an affine open covering $X = \bigcup U_\alpha$ such that the restriction of $\mathbb V$ to each $U_\alpha$ is isomorphic to $\mathbb G^d_a$ over $U_\alpha$.
I assume the $\mathbb G_a$ is the additive group of $\mathbb A^1$, but I am not sure what field $\mathbb A^1$ comes from. Could someone enlighten me?
Thanks ever so much! :)