# Spectral algebras and non-commutative Hodge-to-de Rham degeneration

## TL;DR

This paper revisits and streamlines the proof of the non-commutative Hodge-to-de Rham degeneration theorem, emphasizing the role of spectral algebraic geometry and topology in the proof.

## Contribution

It provides an improved proof of the theorem using spectral algebraic geometry and clarifies the importance of topology in the argument.

## Key findings

- Streamlined proof of the non-commutative Hodge-to-de Rham degeneration theorem.
- Explicit use of spectral algebraic geometry in the proof.
- Explanation of the essential role of topology in the theorem's proof.

## Abstract

We revisit the non-commutative Hodge-to-de Rham Degeneration Theorem of the first author, and present its proof in a somewhat streamlined and improved form that explicitly uses spectral algebraic geometry. We also try to explain why topology is essential to the proof.