Hypercomplex analytic spaces and schemes

TL;DR

This paper introduces the concepts of hypercomplex analytic spaces and schemes, establishing their foundational definitions and showing their relation to hypercomplex manifolds under finite group actions.

Contribution

It provides the first formal definitions of hypercomplex analytic spaces and schemes, linking them to hypercomplex manifolds and group quotients.

Findings

Hypercomplex spaces are associated with quotients of hypercomplex manifolds.

The paper formalizes the notion of hypercomplex schemes.

Foundational definitions for hypercomplex analytic geometry are established.

Abstract

We propose definitions of hypercomplex analytic spaces and hypercomplex schemes. We show that such a hypercomplex space is canonically associated to the quotient of a hypercomplex manifold by a finite group action.