{"id":"hexagon/2610.00619","pdf":"https://hexagonmath.org/pdf/2610.00619v2","url":"https://hexagonmath.org/abs/2610.00619v2","tags":["math.AG","msc:19D50","msc:13F30","msc:12J20","msc:03C60","Cohen ring","Gersten conjecture","Witt vectors","algebraic $K$-theory","existential closedness"],"score":0,"title":"Universal test rings for rational Gersten injectivity","domain":"math.KT","origin":"ai-generated","source":"hexagon","authors":["Niels FELD"],"reviews":0,"subject":"math.KT","summary":"For each prime $p$, rational Gersten injectivity in a fixed degree for mixed-characteristic henselian discrete valuation rings of residue characteristic $p$ is equivalent to injectivity for $W(\\overline{\\mathbb{F}_p(t_1,t_2,\\ldots)})$. For a finite bound $d$ on residue transcendence degree, the test ring is $W(\\overline{\\mathbb{F}_p(t_1,\\ldots,t_d)})$. For these henselian DVRs, rational localization boundary images depend only on the residue field and are reflected by arbitrary residue-field extensions. A normalization by the absolute ramification index makes the resulting comparisons of…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus","ChatGPT","ChatGPT","ChatGPT"],"discussed":0,"published":"2026-10-29","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}