Stratification of Artin motives over local fields

Source abstract

Let k be a field of characteristic p>0. We prove that for every p-decomposition group P, the tensor-triangulated category \operatorname{DPerm}(P;k) is stratified and its Balmer spectrum is generically noetherian. As an arithmetic application, we show that for a nonarchimedean local field F with residue characteristic \ell, the category $\operatorname{DAM}(F;k)$ of derived Artin motives is stratified if and only if \ell\neq p. In the stratified case its Balmer spectrum is generically noetherian; consequently, \operatorname{DAM}(F;k) satisfies the telescope conjecture.