{"paper":{"title":"Picard and Brauer groups of $K(n)$-local spectra via profinite Galois descent","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AT","authors_text":"Itamar Mor","submitted_at":"2023-06-08T17:45:25Z","abstract_excerpt":"Using the pro\\'etale site, we construct models for the continuous actions of the Morava stabiliser group on Morava E-theory, its $\\infty$-category of $K(n)$-local modules, and its Picard spectrum. For the two sheaves of spectra, we evaluate the resulting descent spectral sequences: these can be thought of as homotopy fixed point spectral sequences for the profinite Galois extension $L_{K(n)} \\mathbb S \\to E_n$. We show that the descent spectral sequence for the Morava E-theory sheaf is the $K(n)$-local $E_n$-Adams spectral sequence. The spectral sequence for the sheaf of Picard spectra is clos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.05393","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/2306.05393/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"}