Analysis reveals the infinity-category of synthetic spectra, suggesting modules over a filtered ring spectrum.
We show that the ∞-category of synthetic spectra based on Morava E-theory is generated by the bigraded spheres and identify it with the ∞-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 ∞-categories.
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Barkan et al. (2025) studied this question.
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