On the motivic Segal conjecture

Thomas Gregersen; John Rognes

On the motivic Segal conjecture

Algebraic Topology 2023-08-09 v2 Algebraic Geometry

Authors: Thomas Gregersen , John Rognes

Abstract

We establish motivic versions of the theorems of Lin and Gunawardena, thereby confirming the motivic Segal conjecture for the algebraic group $\mu_\ell$ of $\ell$ -th roots of unity, where $\ell$ is any prime. To achieve this we develop motivic Singer constructions associated to the symmetric group $S_\ell$ and to $\mu_\ell$ , and introduce a delayed limit Adams spectral sequence.

Keywords

motives conjectures and proofs

Cite

@article{arxiv.2302.12659,
  title  = {On the motivic Segal conjecture},
  author = {Thomas Gregersen and John Rognes},
  journal= {arXiv preprint arXiv:2302.12659},
  year   = {2023}
}

Comments

Based on the first author's PhD thesis [Gre13], guided by the second author. This paper has been accepted for publication by the Journal of Topology

On the motivic Segal conjecture

Abstract

Keywords

Cite

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