Quasi-coherent sheaves on the moduli stack of formal groups

Abstract

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.

References in corpus (2)

• On the moduli stack of commutative, 1-parameter formal Lie groups
• Comodule categories and the geometry of the stack of formal groups

Cited by in corpus (10)

• Local duality in algebra and topology
• Ind-abelian categories and quasi-coherent sheaves
• Which abelian tensor categories are geometric?
• On the derived category of quasi-coherent sheaves on an Adams geometric stack
• Analogs of Dirichlet $L$-functions in chromatic homotopy theory
• The Devinatz-Hopkins Theorem via Algebraic Geometry
• Homotopy groups of $E_C^{h{G}_{24}}\wedge A_1$
• Morava K-theory and Filtrations by Powers
• Moduli stack of oriented formal groups and periodic complex bordism
• Moduli stack of oriented formal groups and the chromatic filtration