# Beyond perturbation 1: de Rham spaces

## TL;DR

This paper explores a new approach to defining de Rham spaces using infinity nilpotent elements, resulting in quotients by germs of diagonals rather than formal neighborhoods, offering a different perspective in differential geometry.

## Contribution

It introduces a novel framework for de Rham spaces based on infinity nilpotent elements, contrasting with traditional definitions using usual nilpotents.

## Key findings

- De Rham spaces are quotients by germs of diagonals.
- Using infinity nilpotent elements changes the structure of de Rham spaces.
- The new approach offers a different geometric interpretation.

## Abstract

It is shown that if one uses the notion of infinity nilpotent elements due to Moerdijk and Reyes, instead of the usual definition of nilpotents to define reduced $C^\infty$-schemes, the resulting de Rham spaces are given as quotients by actions of germs of diagonals, instead of the formal neighbourhoods of the diagonals.