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Free, publicly-accessible full text available January 1, 2026
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Kong, Hana Jia; Quigley, J D (, Proceedings of the London Mathematical Society)Abstract We compute the 2‐adic effective slice spectral sequence (ESSS) for the motivic stable homotopy groups of , a motivic analogue of the connective ‐local sphere over prime fields of characteristic not two. Together with the analogous computation over algebraically closed fields, this yields information about the motivic ‐local sphere over arbitrary base fields of characteristic not two. To compute the spectral sequence, we prove several results that may be of independent interest. We describe the ‐differentials in the slice spectral sequence in terms of the motivic Steenrod operations over general base fields, building on analogous results of Ananyevskiy, Röndigs, and Østvær for the very effective cover of Hermitian K‐theory. We also explicitly describe the coefficients of certain motivic Eilenberg–MacLane spectra and compute the ESSS for the very effective cover of Hermitian K‐theory over prime fields.more » « lessFree, publicly-accessible full text available November 1, 2025
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Behrens, Mark; Mahowald, Mark; Quigley, J D (, Geometry & Topology)
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Greenlees, J.; Quigley, J. D. (, Proceedings of the American Mathematical Society, Series B)
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