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Quasi-coherent sheaves on the moduli stack of formal groups

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arxiv 0802.0996 v1 pith:KWQQ5SYR submitted 2008-02-07 math.AT math.AG

Paul G. Goerss This is my paper · ORCID
classification math.ATmath.AG
keywords stackformalgroupsmoduliresultsalgebraicgeometryitself
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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Cited by 4 Pith papers

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  1. Affineness and reconstruction in complex-periodic geometry

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    A new spectral-stack framework shows that many moduli stacks in complex-periodic homotopy theory, including bounded-height oriented formal groups and oriented elliptic curves, are determined by their global sections.

  2. Spectral moduli problems for level structures and an integral Jacquet-Langlands dual of Morava E-theory

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    Derived level structures in spectral algebraic geometry are representable, yielding Jacquet-Langlands spectra and a proposed Jacquet-Langlands dual of Morava E-theory.

  3. Modeling Group Actions on Stacks (Especially the Lubin-Tate Action)

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    A survey codifying geometric modeling and two-tower methods for group actions on formal moduli stacks, with the Lubin-Tate action as the guiding example.

  4. Periodic phenomena in stable motivic homotopy theory

    math.AT 2026-07 unverdicted novelty 2.0 of 10

    A survey of periodic phenomena in stable motivic homotopy theory, organizing known motivic Adams spectral sequence computations and open problems; no new theorem is proven.

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