---
date: 2022-05-10 15:17
modification date: Tuesday 10th May 2022 15:17:36
title: spectral algebraic geometry
aliases:
  - spectral algebraic geometry
  - derived geometry
created: 2022-05-10T15:17
updated: 2023-12-16T00:17
---
- **Derived commutative algebra** plays an important technical role in recent work of Bhatt-Morrow-Scholze and Bhatt-Scholze on integral [p-adic Hodge theory](p-adic%20Hodge%20theory.md).
- Derived algebraic geometry also comes in different flavors, being built out of commutative [DGAs](DGA.md), [simplicial commutative rings](animated%20rings.md), and [E_infty algebras](E_n%20ring%20spectrum.md).
# spectral algebraic geometry

![](attachments/Pasted%20image%2020220510151738.png)

![](attachments/Pasted%20image%2020220510161225.png)