{"paper":{"title":"Finite-coefficient Gersten injectivity fails in ramified mixed characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Niels Feld","submitted_at":"2026-08-05T16:12:07Z","abstract_excerpt":"Let $V$ be a complete discrete valuation ring of mixed characteristic $(0,3)$ in which $3$ is a uniformizer, and put $A=V[[x,y]]/(3+x^2-y^3)$. We construct a nonzero class $a\\in K_2(A;\\mathbf Z/3)$ whose restriction to the fraction field of $A$ is zero. Thus Gersten injectivity for algebraic $K$-theory with $\\mathbf Z/3$-coefficients fails for a two-dimensional ramified regular local ring. The coefficient Bockstein of $a$ is zero, while the map $K_2(A)\\to K_2(F)$ is injective. We also indicate the expected analogous construction for every odd prime. This counterexample does not contradict the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05005","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.05005/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}