{"paper":{"title":"A family completion theorem for tempered cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Leonard Tokic","submitted_at":"2026-08-03T15:31:27Z","abstract_excerpt":"Let ${\\mathbb{G}}$ be an oriented $\\mathbb{P}$-divisible group over a noetherian $\\mathbb{E}_\\infty$-ring $R$, let $G$ be a finite group, and let $\\mathcal{F}$ be a family of subgroups of $G$. We show that completion of $R({\\mathbb{G}})_G$-modules at $\\mathcal{F}$ agrees with algebraic completion at the ideal $I_{\\mathbb{G}}(\\mathcal{F})=\\bigcap_{H\\in\\mathcal{F}}\\mathrm{ker} (\\pi_0R({\\mathbb{G}})^{ G}\\to \\pi_0R({\\mathbb{G}})^{ H}).$ For ${\\mathbb{G}}=\\mu_{\\mathbb{P}^\\infty}$ over $\\mathrm{KU}$ this recovers the family completion theorem of Adams, Haeberly, Jackowski, and May, and for the trivi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.02390","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/2608.02390/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"}