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- W2955882021 abstract "For each prime $p$, we define a $t$-structure on the category $widehat{S^{0,0}}/tautext{-}mathbf{Mod}_{harm}^b$ of harmonic $mathbb{C}$-motivic left module spectra over $widehat{S^{0,0}}/tau$, whose MGL-homology has bounded Chow-Novikov degree, such that its heart is equivalent to the abelian category of $p$-completed $BP_*BP$-comodules that are concentrated in even degrees. We prove that $widehat{S^{0,0}}/tautext{-}mathbf{Mod}_{harm}^b$ is equivalent to $mathcal{D}^b({{BP}_*{BP}text{-}mathbf{Comod}}^{ev})$ as stable $infty$-categories equipped with $t$-structures. As an application, for each prime $p$, we prove that the motivic Adams spectral sequence for $widehat{S^{0,0}}/tau$, which converges to the motivic homotopy groups of $widehat{S^{0,0}}/tau$, is isomorphic to the algebraic Novikov spectral sequence, which converges to the classical Adams-Novikov $E_2$-page for the sphere spectrum $widehat{S^0}$. This isomorphism of spectral sequences allows Isaksen and the second and third authors to compute the stable homotopy groups of spheres at least to the 90-stem, with ongoing computations into even higher dimensions." @default.
- W2955882021 created "2019-07-12" @default.
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- W2955882021 date "2018-09-25" @default.
- W2955882021 modified "2023-09-27" @default.
- W2955882021 title "Motivic $Ctau$-modules and $BP_*BP$-comodules" @default.
- W2955882021 hasPublicationYear "2018" @default.
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