{"paper":{"title":"Witt sheaves and the $\\eta$-inverted sphere spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.KT"],"primary_cat":"math.AT","authors_text":"Alexey Ananyevskiy, Ivan Panin, Marc Levine","submitted_at":"2015-04-19T17:09:25Z","abstract_excerpt":"Ananyevsky has recently computed the stable operations and cooperations of rational Witt theory. These computations enable us to show a motivic analog of Serre's finiteness result:\n  Theorem: Let $k$ be a field. Then $\\pi^{\\mathbb{A}^1}_ n(\\mathbb{S}^- _k )_*$ is torsion for $n > 0$.\n  As an application we define a category of Witt motives over $k$ and show that rationally this category is equivalent to the minus part of $SH(k)_\\mathbb{Q}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04860","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":""},"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"}