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Award ID contains: 2105462

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  1. ; ; (, Proceedings of the American Mathematical Society, Series B)
    We describe in terms of generators and relations the ring structure of the R O ( C 2 ) RO(C_2) -graded C 2 C_2 -equivariant stable stems π<#comment/> ⋆<#comment/> C 2 \pi _\star ^{C_2} modulo the ideal of all nilpotent elements. As a consequence, we also record the ring structure of the homotopy groups of the rational C 2 C_2 -equivariant sphere π<#comment/> ⋆<#comment/> C 2 ( S Q ) \pi _\star ^{C_2}(\mathbb {S}_\mathbb {Q}) . 
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  2. ; ; (, European Mathematical Society Press)
    Beliaev, Dmitry; Smirnov, Stanislav (Ed.)
    We consider the problem of computing the stable homotopy groups of spheres, including applications and history. We describe a new technique that yields streamlined computations through dimension 61 and gives new computations through dimension 90 with very few exceptions. We discuss questions and conjectures for further study, including a new approach to the computation of motivic stable homotopy groups over arbitrary base fields. We provide complete charts for the Adams spectral sequence through dimension 90. 
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    Accepted Manuscript Full Text Available
  3. ; (, European Mathematical Society Magazine)
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  4. ; ; (, Publications mathématiques de l'IHÉS)
    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 $$C\tau $$ C τ and the algebraic Novikov spectral sequence for $$BP_{*}$$ B P ∗ , 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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    Full Text Available 
  5. ; ; ; (, Annals of Mathematics)
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