# Derived category of Finite Spaces and Grothendieck Duality

## TL;DR

This paper explores the derived category of modules on finite ringed spaces, establishing key theorems like Bokstedt-Neeman and Grothendieck duality, and extends these results to schemes and broader ringed spaces.

## Contribution

It introduces fundamental duality results for finite ringed spaces and provides a straightforward method to transfer these results to schemes and other ringed spaces.

## Key findings

- Established Bokstedt-Neeman Theorem for finite ringed spaces
- Proved Grothendieck duality in this context
- Extended results to schemes and generalized to other ringed spaces

## Abstract

We obtain some fundamental results, as Bokstedt-Neeman Theorem and Grothendieck duality, about the derived category of modules on a finite ringed space. Then we see how these results are transfered to schemes in a simple way and generalized to other ringed spaces.