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The $\mathbb{C}$-motivic Adams Spectral Sequence for $s\leq5$

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arxiv 2410.16521 v1 pith:QZCXRK4U submitted 2024-10-21 math.AT

Jordan Benson This is my paper · ORCID
classification math.AT
keywords adamstorsionmathbbmotivicsequencespectralappearbound
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abstract

We determine the $\tau^n$-torsion in the first 5-lines of the $E_2$ page of the $\mathbb{C}$-motivic Adams spectral sequence using the techniques of Burklund-Xu. In particular, every element in this range is either $\tau^1$-torsion or $\tau$-free. We also show that $\tau^n$-torsion elements can appear only in Adams filtration at least $2n+2$ and give further evidence of a possible $3n$ bound.

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  1. Exotic periodic phenomena in the cohomology of the moduli stack of $1$-dimensional formal group laws

    math.AT 2025-04 conditional novelty 6.0 of 10

    New w1-periodic families in C-motivic stable homotopy and in the cohomology of the moduli stack of formal group laws have eta-exponents governed by 2-adic valuations.

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