Moduli stack of oriented formal groups and the chromatic filtration

Abstract

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.

arXiv comment37 pages

References in corpus (7)

• Higher Topos Theory
• The Picard group of topological modular forms via descent theory
• Quasi-coherent sheaves on the moduli stack of formal groups
• Local duality in algebra and topology
• On quasi-categories of comodules and Landweber exactness
• The Devinatz-Hopkins Theorem via Algebraic Geometry
• Moduli stack of oriented formal groups and periodic complex bordism

Cited by in corpus (1)

• Moduli stack of oriented formal groups and cellular motivic spectra over $\mathbf{C}$