Abstract: We define derived level structures in the context of spectral algebraic geometry. By studying the representability of derived relative Cartier divisors, we prove that derived level structures are relative representable by spectral algebraic spaces. Combining this result and Lurie’s work on spectral deformations of p-divisible groups, we get towers of formal spectral Deligne-Mumford stacks. These towers can be viewed as higher categorical analogues of Lubin-Tate towers.
