AI 中文总结
该研究针对特征p>0的域，证明了特定张量三角化范畴的分层性及Balmer谱性质，作为算术应用得出导出阿廷动机范畴分层的充要条件，并由此推导其满足望远镜猜想。
AI 中文摘要
设k是特征p>0的域，我们证明对每个p-分解群P，张量三角化范畴DPerm(P;k)是分层的，且其Balmer谱是一般诺特的。作为算术应用，我们表明对剩余特征为ℓ的非阿基米德局部域F，导出阿廷动机范畴DAM(F;k)分层当且仅当ℓ≠p；在分层情形下，其Balmer谱是一般诺特的，因此DAM(F;k)满足望远镜猜想。
英文摘要
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.
Comments31 pages
