{"paper":{"title":"The infinitesimal subgroup of interpretable groups in some dp-minimal valued fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Assaf Hasson, Ya'acov Peterzil, Yatir Halevi","submitted_at":"2025-02-12T07:07:20Z","abstract_excerpt":"We continue our local analysis of groups interpretable in various dp-minimal valued fields, as introduced in [8]. We associate with every infinite group $G$ interpretable in those fields an infinite type-definable infinitesimal subgroup $\\nu(G)$, generated by the four infinitesimal subgroups $\\nu_D(G)$ associated with the distinguished sorts $K$, $\\textbf{k}$, $\\Gamma$ and $K/\\mathcal{O}$.\n  To show that $\\nu(G)$ is type-definable, we show that the resulting subgroups $\\nu_D(G)$ commute with each other as $D$ ranges over the four distinguished sorts. We then study the basic properties of $\\nu("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.08163","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/2502.08163/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"}