It was proved by the first-named author and Zubkov [13] that given an affine algebraic supergroup \( \mathbbm{G} \) and a closed sub-supergroup ℍ over an arbitrary field of characteristic ≠ 2, the faisceau \( \mathbbm{G}\tilde{/}\mathrm{\mathbb{H}} \) (in the fppf topology) is a superscheme, and is, therefore, the quotient superscheme \( \mathbbm{G}/\mathrm{\mathbb{H}} \), which has some desirable properties, in fact. We reprove this, by constructing directly the latter superscheme \( \mathbbm{G}/\mathrm{\mathbb{H}} \). Our proof describes explicitly the structure sheaf of \( \mathbbm{G}/\mathrm{\mathbb{H}} \), and reveals some new geometric features of the quotient, that include one which was desired by Brundan [2], and is shown in general, here for the first time.

第一作者和祖布科夫[13]证明在给定的特征≠2的任意场上，给出了一个仿射代数超群\（\ mathbbm {G} \）和一个封闭的子超群the，即faisceau \（\ mathbbm {G} \ tilde {/} \ mathrm {\ mathbb {H}} \）（在fppf拓扑中）是一个超级方案，因此是商超方案\（\ mathbbm {G} / \ mathrm {\实际上，mathbb {H}} \）具有一些理想的属性。我们通过直接构造后一个超级方案\（\ mathbbm {G} / \ mathrm {\ mathbb {H}} \）来证明这一点。我们的证明明确描述了\（\ mathbbm {G} / \ mathrm {\ mathbb {H}} \）的结构层，并揭示了商的一些新几何特征，其中包括Brundan [2]所期望的几何特征，并在此处首次进行了概括显示。