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Stratification of Artin motives over local fields

  • Peng Xu
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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 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.

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Cite

BibTeXRIS
BibTeX
@misc{xu2026stratification,
  title = {{Stratification of Artin motives over local fields}},
  author = {Peng Xu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03514},
  eprint = {2609.03514},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03514},
}
RIS
TY  - UNPB
TI  - Stratification of Artin motives over local fields
AU  - Peng Xu
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03514
UR  - https://arxiv.org/abs/2609.03514
AB  - 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 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.
ER  -