Abstract
Using techniques in motivic homotopy theory, especially the theorem of Gheorghe, the second and the third author on the isomorphism between motivic Adams spectral sequence for \(C\tau \) and the algebraic Novikov spectral sequence for \(BP_{*}\), we compute the classical and motivic stable homotopy groups of spheres from dimension 0 to 90, except for some carefully enumerated uncertainties.
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The first author was supported by NSF grants DMS-1606290 and DMS-1904241. The second author was supported by grants NSFC-11801082, NSFC-12226002, Shanghai Rising-Star Program 20QA1401600, and Shanghai Pilot Program for Basic Research-FuDan University 21TQ1400100(21TQ002). The third author was supported by NSF grants DMS-1810638 and DMS-2105462. Many of the associated machine computations were performed on the Wayne State University Grid high performance computing cluster.
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Isaksen, D.C., Wang, G. & Xu, Z. Stable homotopy groups of spheres: from dimension 0 to 90. Publ.math.IHES 137, 107–243 (2023). https://doi.org/10.1007/s10240-023-00139-1
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DOI: https://doi.org/10.1007/s10240-023-00139-1