Universal ringed spaces

TL;DR

This paper develops a framework for constructing classical geometric spaces like affine, projective, and Grassmannians within the category of ringed spaces, linking finite posets and sheaves of rings to these structures.

Contribution

It introduces a method to realize key geometric spaces as ringed spaces and connects finite posets and sheaves to these constructions, expanding the categorical understanding.

Findings

Affine, projective spaces, and Grassmannians constructed as ringed spaces.

Finite posets and sheaves of rings naturally appear in these constructions.

Provides a categorical perspective on classical geometric objects.

Abstract

We construct affine spaces, projective spaces and grassmannians in the ca\-te\-gory of ringed spaces. We show how finite posets and sheaves of rings on them appear in a natural way.