Cellularity of Chromatic Synthetic Spectra

TL;DR

This paper demonstrates that the $ abla$-category of synthetic spectra based on Morava E-theory is generated by bigraded spheres and is equivalent to modules over a filtered ring spectrum, using a new method involving t-structures.

Contribution

It introduces a general method for constructing filtered deformations from t-structures on symmetric monoidal stable $ abla$-categories, applied to synthetic spectra.

Findings

Synthetic spectra are generated by bigraded spheres.

Equivalence with modules over a filtered ring spectrum is established.

A new method for filtered deformations from t-structures is developed.

Abstract

We show that the $\infty$-category of synthetic spectra based on Morava E-theory is generated by the bigraded spheres and identify it with the $\infty$-category of modules over a filtered ring spectrum. The latter we show using a general method for constructing filtered deformations from t-structures on symmetric monoidal stable $\infty$-categories.