Pure and Applied Mathematics Quarterly

Volume 16 (2020)

Number 5

Categorical representation of superschemes

Pages: 1635 – 1672

DOI: https://dx.doi.org/10.4310/PAMQ.2020.v16.n5.a10


Yasuhiro Wakabayashi (Department of Mathematics, Tokyo Institute of Technology, Meguro-ku, Tokyo, Japan)


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.


superscheme, supersymmetry

2010 Mathematics Subject Classification

Primary 81R60. Secondary 17A70.

The author was partially supported by the Grant-in-Aid for Scientific Research (KAKENHI No. 18K13385).

Received 19 September 2019

Accepted 4 May 2020

Published 17 February 2021