{"paper":{"title":"Wilson Spaces, Snaith Constructions, and Elliptic Orientations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Allen Yuan, Hood Chatham, Jeremy Hahn","submitted_at":"2019-10-10T14:46:11Z","abstract_excerpt":"We construct a canonical family of even periodic $\\mathbb{E}_{\\infty}$-ring spectra, with exactly one member of the family for every prime $p$ and chromatic height $n$. At height $1$ our construction is due to Snaith, who built complex $K$-theory from $\\mathbb{CP}^{\\infty}$. At height $2$ we replace $\\mathbb{CP}^{\\infty}$ with a $p$-local retract of $\\mathrm{BU} \\langle 6 \\rangle$, producing a new theory that orients elliptic, but not generic, height $2$ Morava $E$-theories.\n  In general our construction exhibits a kind of redshift, whereby $\\mathrm{BP}\\langle n-1 \\rangle$ is used to produce a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.04616","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/1910.04616/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"}