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arXiv · 2508.09900

$C^\infty$-superrings and $C^\infty$-superschemes

Cristian Danilo Olarte·Pedro Rizzo·Alexander Torres-Gomez
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Abstract

This paper develops a theory of $C^\infty$-superrings and their associated $C^\infty$-superschemes. We prove a key equivalence between the category of fair affine $C^\infty$-superschemes and the category of fair $C^\infty$-superrings. We place special emphasis on split $C^\infty$-superrings, which generalize the function algebras of supermanifolds and serve as building blocks for more complex, non-split structures.

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Cristian Danilo Olarte, Pedro Rizzo, Alexander Torres-Gomez. 2025-08-13. $C^\infty$-superrings and $C^\infty$-superschemes. https://arxiv.org/abs/2508.09900

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