Formal Superschemes over Fields: Basic Theory

TL;DR

This paper develops the foundational theory of formal superschemes over fields, introducing key concepts and establishing fundamental properties, including descent and fiber dimension theorems, in the supersymmetric context.

Contribution

It introduces the notion of formal superschemes and proves foundational theorems on morphisms, advancing the mathematical framework of supersymmetric algebraic geometry.

Findings

Established the notion of formal superschemes.

Proved a faithfully flat descent theorem for formal superschemes.

Derived a fiber dimension-type theorem in the supersymmetric setting.

Abstract

This paper develops the basic theory of formal schemes over fields in the supersymmetric setting. We introduce the notion of a formal superscheme and investigate some of its fundamental properties. Particular emphasis is placed on the study of morphisms between formal superschemes, for which we establish a faithfully flat descent theorem and a fiber dimension-type theorem.