---
title: "Stratification of Artin motives over local fields"
authors:
  - "Peng Xu"
year: 2026
venue: "arXiv:math.CT"
arxiv: "2609.03514"
doi: null
source: "https://arxiv.org/abs/2609.03514"
topics:
  - "curiosity"
  - "maths-foundations"
seed_rank: 1615
seed_batch: "curiosity-2026-09-07"
reviewed: "2026-09-07"
pool: "maths-foundations"
relevance_score: 10
lineage: tensor-triangular-geometry
cites:
  - title: "Stratification of Artin motives over local fields"
    url: "https://arxiv.org/abs/2609.03514"
    year: 2026
    arxiv: "2609.03514"
    doi: null
see:
  - "1584-generalized-telescope-conjecture"
  - "1614-another-counterexample-to-the-nerves-of-steel-conjecture"
---

# Stratification of Artin motives over local fields

## One-sentence takeaway

Permutation motives for p-decomposition groups are Balmer-stratified with generically noetherian spectrum — tt-geometry meeting local-field arithmetic.

## Why it's lovely

Why you might love this: Artin/permutation motives, local fields, and Balmer stratification in one package. After a day of spectrum counterexamples, here is a positive stratification theorem with an arithmetic payoff for nonarchimedean local fields.

## Key ideas

- For each p-decomposition group P, DPerm(P;k) is stratified in the Balmer sense.
- Balmer spectrum generically noetherian.
- Arithmetic application to motives over nonarchimedean local fields.
- Companion tone to Nerves-of-Steel counterexamples: when stratification *does* hold.

## Caveats

Characteristic-p / local-field setting; not a general tt-stratification machine for arbitrary motives.

## Implications for Broadside

Concrete Balmer stratification in an arithmetic category — the constructive twin of spectrum-comparison drama on the same shelf.

## Links

- arXiv abs: https://arxiv.org/abs/2609.03514
- PDF: https://arxiv.org/pdf/2609.03514.pdf