{"paper":{"title":"On Andr\\'e periods of mixed Tate motives","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ishai Dan-Cohen","submitted_at":"2025-02-24T18:31:36Z","abstract_excerpt":"In this note, we show that the $p$-adic periods of motives introduced recently by Ancona and Fr\\u{a}\\c{t}il\\u{a} (``Andr\\'e periods'') reduce to the classically studied notion in the case of Mixed Tate motives. We also connect Andr\\'e periods with Coleman integration by observing that the Frobenius-fixed de Rham paths of Besser and Vologodsky come from motivic paths in characteristic $p$ (unconditionally in the mixed Tate setting, conditionally in general). We use this to realize special values of $p$-adic multiple polylogarithms as Andr\\'e periods in a concrete way."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.17404","kind":"arxiv","version":2},"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/2502.17404/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"}