# Chromatic structures in stable homotopy theory

## TL;DR

This survey explores how the global structure of the stable homotopy category leads to the chromatic filtration, highlighting computational tools and recent advances in local chromatic homotopy theory with illustrative examples.

## Contribution

It provides a comprehensive overview of the chromatic filtration in stable homotopy theory and discusses recent computational methods and developments.

## Key findings

- Overview of the chromatic filtration structure
- Discussion of computational tools in local chromatic homotopy theory
- Presentation of recent advances and explicit examples

## Abstract

In this survey, we review how the global structure of the stable homotopy category gives rise to the chromatic filtration. We then discuss computational tools used in the study of local chromatic homotopy theory, leading up to recent developments in the field. Along the way, we illustrate the key methods and results with explicit examples.