Categorical representation of superschemes

TL;DR

This paper extends the categorical reconstruction of schemes to superschemes, showing that locally noetherian superschemes can be recovered from their associated categories of noetherian superschemes, generalizing Mochizuki's classical result.

Contribution

It introduces a supergeometric generalization of Mochizuki's scheme reconstruction theorem, establishing categorical equivalences for superschemes.

Findings

Superschemes can be reconstructed from their categories of noetherian superschemes.

The reconstruction is unique up to certain categorical equivalences.

Generalizes classical scheme reconstruction results to supergeometry.

Abstract

In the present paper, we prove that a locally noetherian superscheme $X^\circledS$ may be reconstructed (up to certain equivalence) category-theoretically from the category of noetherian superschemes over $X^\circledS$. This result is a supergeometric generalization of the result proved by Shinichi Mochizuki concerning categorical reconstruction of schemes.