{"paper":{"title":"Tate-valued Characteristic Classes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Kiran Luecke, Shachar Carmeli","submitted_at":"2025-03-15T13:33:20Z","abstract_excerpt":"We define a projective variant of classical complex orientation theory. Using this, we construct a map of spectra which lifts the total Chern class, providing an alternative answer to an old question of Segal \\cite{segal}, previously answered by Lawson et al \\cite{lawsonetal}. We also lift and generalize the ``sharp'' construction of Ando-French-Ganter \\cite{afg} to an operation on arbitrary $\\EE_\\infty$-complex orientations, thereby providing a rich source of new $\\EE_\\infty$-orientations for commutative ring spectra. In particular we give an $\\EE_\\infty$-lift of the Jacobi orientation, a gen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.12134","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/2503.12134/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"}