An illustration of formal moduli problems with differential graded Lie algebras

TL;DR

This paper offers an accessible introduction to formal moduli problems and their relationship with differential graded Lie algebras within derived algebraic geometry, based on Jacob Lurie's foundational work.

Contribution

It provides a clear, organized exposition aimed at non-experts, clarifying complex concepts without presenting new research.

Findings

Clarifies the connection between formal moduli problems and dg Lie algebras

Serves as an educational resource for derived algebraic geometry

Simplifies complex topics for non-expert readers

Abstract

This article provides an exposition to the topic of formal moduli problems, emphasizing its connections with differential graded Lie algebras, and mainly following from Jacob Lurie's DAG X: Formal Moduli Problems. As such, this paper should not be viewed as a presentation of original work, but rather a concise introduction to the subject in the form of a set of organized notes. I hoped to make this paper feel welcoming and insightful for the non-expert enjoyer of derived algebraic geometry, like myself. Enjoy!