# Homotopical Algebraic Context over Differential Operators

## TL;DR

This paper demonstrates that the category of non-negatively graded chain complexes of differential operator modules over a smooth affine algebraic variety can be integrated into a homotopical algebraic framework, extending previous theoretical work.

## Contribution

It establishes a homotopical algebraic context for chain complexes of D-modules over smooth affine varieties, building on and extending prior theoretical foundations.

## Key findings

- Category of chain complexes of D-modules fits into homotopical algebraic context
- Extends Toen and Vezzosi's framework to D-module categories
- Provides a new perspective for homotopical methods in algebraic geometry

## Abstract

Building on previous works, we show that the category of non-negatively graded chain complexes of $D_X$-modules -- where $X$ is a smooth affine algebraic variety over an algebraically closed field of characteristic zero -- fits into a homotopical algebraic context in the sense of Toen and Vezzosi.