Group superschemes

We develop a general theory of algebraic group superschemes, which are not necessarily affine. Our key result is a category equivalence between those group superschemes and Harish-Chandra pairs, which generalizes the result known for affine algebraic group superschemes. Then we present the applications, including the Barsotti-Chevalley Theorem in the super context, and an explicit construction of the quotient superscheme $\mathbb{G}\mathrm{/}\mathbb{H}$ of an algebraic group superscheme $\mathbb{G}$ by a group super-subscheme $\mathbb{H}$.