There is a notion of smooth stack in "homotopical algebraic geometry 2" and a notion of a cotangent complex for certain kinds of stacks (including representable stacks). I have two questions.
Is the moduli stack of one dimensional commutative formal groups of height less than or equal to $n$ smooth in this sense?
Is the formal moduli stack of deformations of a one dimensional commutative formal group over a perfect field of characteristic $p$ of height equal to $n$ smooth in this sense? Here I mean the quotient stack of deformations by the action of the stabilizer group.
It seems to me that (2) should be true as this is the "ind-'etale" quotient of Lubin-Tate. Question (1) should be true because of locality for smoothness, but a reference to the result (or at least the relevant tools in the concrete from) would be nice.