2018/08/17 by Masuoka, Akira, Takahashi, Yuta · 1 citation
#14L15 #14M30 #16T05 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1808.05753
It was proved by the first-named author and Zubkov [13] that given an affine algebraic supergroup \mathbbG and a closed sub-supergroup ℍ over an arbitrary field of characteristic ≠ 2, the faisceau \mathbbG / ℍ (in the fppf topology) is a superscheme, and is, therefore, the quotient superscheme \mathbbG/ℍ, which has desirable properties, in fact. We reprove this, by constructing directly the latter superscheme \mathbbG/ℍ. Our proof describes explicitly the structure sheaf of \mathbbG/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.