{"paper":{"title":"On the derived Tate curve and global smooth Tate $K$-theory","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.AG","math.KT"],"primary_cat":"math.AT","authors_text":"Jack Morgan Davies, Sil Linskens","submitted_at":"2025-03-06T14:42:39Z","abstract_excerpt":"The interplay between equivariant stable homotopy theory and spectral algebraic geometry is used to construct a derived Tate curve over $\\mathrm{KU}((q))$, a lift of the classical elliptic curve of Tate over $\\mathbf{Z}((q))$. Applications of both an algebro-geometric and a topological flavour follow. First, we construct a spectral algebro-geometric model for the compactification of the moduli stack of oriented elliptic curves, giving a canonical choice of holomorphic topological $q$-expansion map. Then we define globally equivariant forms of Tate $K$-theory $\\mathbf{KO}((q))$ and $\\mathbf{KU}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.04494","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/2503.04494/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"}