{"paper":{"title":"Duality of analytic Hopf algebras and the Amice transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Analytic Hopf algebras for Amice duality can be built over any Banach ring without depending on a prime p.","cross_cats":["math.AG","math.FA"],"primary_cat":"math.NT","authors_text":"Luca Collauto","submitted_at":"2026-05-15T15:28:06Z","abstract_excerpt":"We construct global versions of the analytic Hopf algebras used in the $p$-adic Fourier theory of Amice and Mahler over a general Banach ring, independently of the choice of prime $p$. This is done by generalising K\\\"othe echelon and coechelon spaces to an arbitrary base Banach ring $R$ and proving reflexivity and nuclearity results. We show how to define an analytic Hopf algebra structure on them and investigate their duality theory. The particular case of the Hopf algebra of analytic functions converging on the open unit disk around $1$ and its dual is studied in detail. Amice duality is rec"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"When R is the ring of integers with the trivial norm, we obtain a global analytic version of Amice duality that does not depend on p.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The generalized Kothe echelon and coechelon spaces over an arbitrary Banach ring R satisfy the reflexivity and nuclearity properties required to support an analytic Hopf algebra structure and its duality theory.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Constructs global analytic Hopf algebras on generalized Kothe spaces over arbitrary Banach rings, proves reflexivity and nuclearity, and obtains a p-independent version of Amice duality via base change.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Analytic Hopf algebras for Amice duality can be built over any Banach ring without depending on a prime p.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"3af5f327655818d8378870291146ac5bb6e9cb1c7c085ba91f5f1577690824d5"},"source":{"id":"2605.16063","kind":"arxiv","version":1},"verdict":{"id":"df78a0de-b980-4117-95a8-f0b21a20f38b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:58:51.389414Z","strongest_claim":"When R is the ring of integers with the trivial norm, we obtain a global analytic version of Amice duality that does not depend on p.","one_line_summary":"Constructs global analytic Hopf algebras on generalized Kothe spaces over arbitrary Banach rings, proves reflexivity and nuclearity, and obtains a p-independent version of Amice duality via base change.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The generalized Kothe echelon and coechelon spaces over an arbitrary Banach ring R satisfy the reflexivity and nuclearity properties required to support an analytic Hopf algebra structure and its duality theory.","pith_extraction_headline":"Analytic Hopf algebras for Amice duality can be built over any Banach ring without depending on a prime p."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16063/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T19:31:18.997434Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:10:49.004335Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:41.547915Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T16:41:55.519096Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"58f06a8ce6bcb056d30198c57c9e1ae058b7f0b5d931d9b8a740332a5671d88a"},"references":{"count":17,"sample":[{"doi":"","year":2007,"title":"2007 , doi =","work_id":"ff80e468-3226-4633-84a7-098e3309ac19","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1016/j.jnt.2015.10.023","year":2016,"title":"2016 , issn =","work_id":"9ad2a561-0e67-42b7-90d2-0ed836ea70e5","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"Oren Ben-Bassat and Kobi Kremnizer , journal=. 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