{"paper":{"title":"The Chromatic Nullstellensatz","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"Allen Yuan, Robert Burklund, Tomer M. Schlank","submitted_at":"2022-07-20T14:13:40Z","abstract_excerpt":"We show that Lubin--Tate theories attached to algebraically closed fields are characterized among $T(n)$-local $\\mathbb{E}_{\\infty}$-rings as those that satisfy an analogue of Hilbert's Nullstellensatz. Furthermore, we show that for every $T(n)$-local $\\mathbb{E}_{\\infty}$-ring $R$, the collection of $\\mathbb{E}_\\infty$-ring maps from $R$ to such Lubin-Tate theories jointly detect nilpotence. In particular, we deduce that every non-zero $T(n)$-local $\\mathbb{E}_{\\infty}$-ring $R$ admits an $\\mathbb{E}_\\infty$-ring map to such a Lubin-Tate theory. As consequences, we construct $\\mathbb{E}_{\\inf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.09929","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/2207.09929/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"}