Introducci\'on a los D-m\'odulos

TL;DR

This paper provides an introductory overview of the theory of modules over rings of differential operators on smooth algebraic varieties, aimed at mathematicians interested in algebraic geometry and differential operators.

Contribution

It offers a foundational exposition on D-modules in the context of smooth algebraic varieties, bridging algebraic and differential geometric perspectives.

Findings

Introduces the basic concepts of D-modules.

Explains the structure of rings of differential operators.

Provides examples relevant to algebraic geometry.

Abstract

Estas notas son las memorias del cursillo dictado en el XXII Congreso Colombiano de Matem\'aticas en la Universidad del Cauca en Popay\'an - Colombia. El objetivo de este escrito es brindar un acercamiento a la teor\'ia de m\'odulos sobre el anillo de operadores diferenciales de una variedad algebraica suave. These are the lecture notes of a short course given at the XXII Colombian Congress of Mathematics held at Universidad del Cauca in Popay\'an - Colombia. The aim of this paper is to provide an introduction to the theory of modules over rings of differential operators over a smooth algebraic variety.