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• W3118171261 abstract "Let $kq$ denote the very effective cover of Hermitian K-theory. We apply the $kq$-based motivic Adams spectral sequence, or $kq$-resolution, to computational motivic stable homotopy theory. Over base fields of characteristic not two, we prove that the $n$-th stable homotopy group of motivic spheres is detected in the first $n$ lines of the $kq$-resolution, thereby reinterpreting results of Morel and R{o}ndigs-Spitzweck-{O}stv{ae}r in terms of $kq$ and $kq$-cooperations. Over algebraically closed fields of characteristic 0, we compute the ring of $kq$-cooperations modulo $v_1$-torsion, establish a vanishing line of slope $1/5$ in the $E_2$-page, and completely determine the $0$- and $1$- lines of the $kq$-resolution. This gives a full computation of the $v_1$-periodic motivic stable stems and recovers Andrews and Miller's calculation of the $eta$-periodic $mathbb{C}$-motivic stable stems. We also construct a motivic connective $j$ spectrum and identify its homotopy groups with the $v_1$-periodic motivic stable stems. Finally, we propose motivic analogs of Ravenel's Telescope and Smashing Conjectures and present evidence for both." @default.
• W3118171261 created "2021-01-05" @default.
• W3118171261 creator A5026487942 @default.
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• W3118171261 date "2019-05-28" @default.
• W3118171261 modified "2023-09-27" @default.
• W3118171261 title "$kq$-Resolutions I" @default.
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