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Moduli stack of oriented formal groups and the chromatic filtration

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arxiv 2111.15202 v1 pith:N47CQXN6 submitted 2021-11-30 math.AT math.AG

Moduli stack of oriented formal groups and the chromatic filtration

Rok Gregoric This is my paper
classification math.AT math.AG
keywords chromaticfiltrationformalgroupsmodulistackclassicallocalization
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We define a filtration by open substacks on the non-connective spectral moduli stack of formal oriented groups, which simultaneously encodes and relates the chromatic filtration of spectra and the height stratification of the classical moduli stack of formal groups. Using this open filtration, we express various classical constructions in chromatic homotopy theory, such as chromatic localization, the monochromatic layer, and $K(n)$-localization, in terms of restriction and completion of sheaves in non-connective spectral algebraic geometry.

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  1. Affineness and reconstruction in complex-periodic geometry

    math.AT 2025-10 accept novelty 8.0

    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.