Formal moduli problems with cohomological constraints

TL;DR

This paper extends the correspondence between formal moduli problems and dg Lie algebras to include cohomological constraints, establishing an equivalence with derived cohomology jump functors and answering an open question.

Contribution

It generalizes the Lurie-Pridham correspondence to incorporate cohomological conditions, linking formal moduli problems with derived cohomology jump functors.

Findings

Established an equivalence between constrained formal moduli problems and cohomology jump functors

Extended the Lurie-Pridham correspondence to a broader context with cohomological constraints

Provided an affirmative answer to a question by Budur and Wang

Abstract

We aim to generalize Lurie-Pridham's famous $\infty$-correspondence between formal moduli problems and differential graded Lie algebras to the context where some cohomological conditions are imposed. Specifically, a natural equivalence between formal moduli problems with cohomological constraints and derived cohomology jump functors is provided, thereby answering affirmatively a question posed by N. Budur and B. Wang in \cite{1}.