# group scheme neither affine, nor an abelian variety

Does there exist a group scheme of finite type over a field $k$ , which is neither affine, nor an abelian variety?

• Related entry: mathoverflow.net/questions/43529/… May 18, 2011 at 13:22
• As my answer indicates, it's unclear precisely what you mean by your parenthetic statement. Being an affine group scheme doesn't imply having a realization as a matrix group. Certainly you want to consider the motivating examples mentioned in Brian Conrad's cited paper. May 18, 2011 at 20:26