| We attempt the beginnings of a general algebro-geometric study of the moduli stack of commutative, 1-parameter formal Lie groups, in full comportment with the modern foundations of algebraic geometry. We emphasize the pro-algebraic structure of this stack: it is the inverse limit, over varying n, of moduli stacks of n-buds, and these latter stacks are algebraic. Our main theorems pertain to the height stratification relative to fixed prime p on the stacks of formal Lie groups and of n-buds. Notably, we show that the stack of n-buds of height ≥h is smooth over Fp of dimension -h, and we obtain a characterization of the stratum of formal Lie groups of (exact) height h as an inverse limit of classifying stacks of certain finite etale algebraic groups. |
