Thomas Gregersen

On the motivic Segal conjecture

We establish motivic versions of the theorems of Lin and Gunawardena, thereby confirming the motivic Segal conjecture for the algebraic group $μ_\ell$ 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 $μ_\ell$, and introduce a delayed limit Adams spectral sequence.