The infinitesimal structure of any moduli space in characteristic zero is controlled by a differential graded Lie algebra. This far-reaching generalization of Kodaira-Spencer theory was established by Lurie and Pridham, based on previous work of Deligne, Drinfeld, Feigin, Hinich, and others. In this talk, I will explain how to generalize the above statement to finite and mixed characteristic.

This is joint work with Akhil Mathew.