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Stable comodule deformations and the synthetic Adams-Novikov spectral sequence
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Stable comodule deformations and the synthetic Adams-Novikov spectral sequence
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We study the Adams-Novikov spectral sequence in $\mathbb{F}_p$-synthetic spectra, computing the synthetic analogs of $\mathrm{BP}$ and its cooperations to identify the synthetic Adams-Novikov $\mathrm{E}_2$-page, computed in a range with a synthetic algebraic Novikov spectral sequence. We then identify deformations associated to the Cartan-Eilenberg and algebraic Novikov spectral sequences in terms of stable comodule categories, categorifying an algebraic Novikov spectral sequence result of Gheorghe-Wang-Xu. We then apply Isaksen-Wang-Xu methods in $\mathbb{F}_2$-synthetic spectra to deduce differentials in the $p=2$ synthetic Adams-Novikov for the sphere, producing almost entirely algebraic computations through the 45-stem.
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Cited by 1 Pith paper
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Periodic phenomena in stable motivic homotopy theory
A survey of periodic phenomena in stable motivic homotopy theory, organizing known motivic Adams spectral sequence computations and open problems; no new theorem is proven.
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