{"paper":{"title":"Profinite equivariant spectra and their tensor-triangular geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RT"],"primary_cat":"math.AT","authors_text":"David Barnes, Scott Balchin, Tobias Barthel","submitted_at":"2024-01-03T18:38:26Z","abstract_excerpt":"We study the tensor-triangular geometry of the category of equivariant $G$-spectra for $G$ a profinite group, $\\mathsf{Sp}_G$. Our starting point is the construction of a ``continuous'' model for this category, which we show agrees with all other models in the literature. We describe the Balmer spectrum of finite $G$-spectra up to the ambiguity that is present in the finite group case; in particular, we obtain a thick subcategory theorem when $G$ is abelian. By verifying the bijectivity hypothesis for $\\mathsf{Sp}_G$, we prove a nilpotence theorem for all profinite groups.\n  Our study then mov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.01878","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/2401.01878/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"}