$C^\infty$-superrings and $C^\infty$-superschemes
Algebraic Geometry
2025-12-01 v2 Differential Geometry
Rings and Algebras
Abstract
This paper develops a theory of -superrings and their associated -superschemes. We prove a key equivalence between the category of fair affine -superschemes and the category of fair -superrings. We place special emphasis on split -superrings, which generalize the function algebras of supermanifolds and serve as building blocks for more complex, non-split structures.
Cite
@article{arxiv.2508.09900,
title = {$C^\infty$-superrings and $C^\infty$-superschemes},
author = {Cristian Danilo Olarte and Pedro Rizzo and Alexander Torres-Gomez},
journal= {arXiv preprint arXiv:2508.09900},
year = {2025}
}
Comments
Compared to the first version, we only replaced a comment on page 10 regarding the category of $C^\infty$-Superrings. In the initial version, we intended to state that the category of modules over $C^\infty$-Superrings was abelian, but it was mistakenly written that the category of $C^\infty$-Superrings itself was abelian (which is incorrect)