{"paper":{"title":"THH(Z) and the image of J","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.KT"],"primary_cat":"math.AT","authors_text":"Arpon Raksit, Sanath K. Devalapurkar","submitted_at":"2025-05-04T19:01:32Z","abstract_excerpt":"Let $p$ be an odd prime number and $\\mathrm{j}_p$ the $p$-complete connective image of J spectrum. We establish an equivalence of cyclotomic $\\mathbb{E}_\\infty$-rings $\\mathrm{THH}(\\mathbb{Z})^{\\wedge}_p \\simeq \\mathrm{sh}(\\mathrm{j}_p^{\\mathrm{triv}})$ and an equivalence of $\\mathbb{E}_\\infty$-rings $\\mathrm{TP}(\\mathbb{Z})^{\\wedge}_p \\simeq \\mathrm{j}_p^{\\mathrm{t}\\mathrm{S}^1}$. We also record a few applications of this: a new perspective, with some new information, on the description of $\\mathrm{TC}(\\mathbb{Z})^{\\wedge}_p$ as a spectrum; height $1$ analogues of the fiber squares of Antieau"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.02218","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/2505.02218/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"}