Chromatic applications of spectral algebraic geometry

Date

2023-04-21

Authors

Gregoric, Rok

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Abstract

We recast many central results in chromatic homotopy theory as statements in spectral algebraic geometry, as concerning certain spectral enhancements of the stack of formal groups and its variants. This perspective allows us to formalize many folklore analogies between chromatic homotopy and algebraic geometry going back to Morava, Hopkins, and others. We also use it to provide a spectral-algebro-geometric explanation for the [tau]-deformation phenomena of Gheorghe, Isaksen, Wang, Xu, exhibiting a connection to motivic and synthetic homotopy theory.

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