Quotient sheaves of algebraic supergroups are superschemes

Abstract

To generalize some fundamental results on group schemes to the super context, we study the quotient sheaf $G\widetilde{/}H$ of an algebraic supergroup $G$ by its closed supersubgroup $H$, in arbitrary characteristic $\ne$ 2. Our main theorem states that $G\widetilde{/}H$ is a Noetherian superscheme. This together with derived results give positive answers to interesting questions posed by J. Brundan.

Revised the manuscript, improving the exposition and correcting typos, 40 pages; the final version accepted for publication

Cited by in corpus (4)

• Cohomological finite generation for restricted Lie superalgebras and finite supergroup schemes
• Borel-Weil Theorem for Algebraic Supergroups
• Algebraic supergroups and Harish-Chandra pairs over a commutative ring
• The Twofold Way of Super Holonomy