Universal test rings for rational Gersten injectivity
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…
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