{"paper":{"title":"$p$-adic dimensions in symmetric tensor categories in characteristic $p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.QA"],"primary_cat":"math.RT","authors_text":"Nate Harman, Pavel Etingof, Victor Ostrik","submitted_at":"2015-10-14T22:42:25Z","abstract_excerpt":"To every object $X$ of a symmetric tensor category over a field of characteristic $p>0$ we attach $p$-adic integers $\\text{Dim}_+(X)$ and $\\text{Dim}_-(X)$ whose reduction modulo $p$ is the categorical dimension $\\text{dim}(X)$ of $X$, coinciding with the usual dimension when $X$ is a vector space. We study properties of $\\text{Dim}_{\\pm}(X)$, and in particular show that they don't always coincide with each other, and can take any value in $\\mathbb{Z}_p$. We also discuss the connection of $p$-adic dimensions with the theory of $\\lambda$-rings and Brauer characters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04339","kind":"arxiv","version":5},"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/1510.04339/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"}