  The central aim of this monograph is to provide decomposition results for
quasi-coherent sheaves on the moduli stack of one-dimensional formal groups.
These results will be based on the geometry of the stack itself, particularly
the height filtration and an analysis of the formal neighborhoods of the
geometric points. The main theorems are algebraic chromatic convergence results
and fracture square decompositions. There is a major technical hurdle in this
story, as the moduli stack of formal groups does not have the finitness
properties required of an algebraic stack as usually defined. This is not a
conceptual problem, but in order to be clear on this point and to write down a
self-contained narrative, I have included a great deal of discussion of the
geometry of the stack itself, giving various equivalent descriptions.
