{"paper":{"title":"On the Orientability of the Slice Filtration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT"],"primary_cat":"math.KT","authors_text":"Pablo Pelaez","submitted_at":"2010-09-21T15:00:54Z","abstract_excerpt":"Let $X$ be a Noetherian separated scheme of finite Krull dimension. We show that the layers of the slice filtration in the motivic stable homotopy category $\\stablehomotopy$ are strict modules over Voevodsky's algebraic cobordism spectrum. We also show that the zero slice of any commutative ring spectrum in $\\stablehomotopy$ is an oriented ring spectrum in the sense of Morel, and that its associated formal group law is additive. As a consequence, we get that with rational coefficients the slices are in fact motives in the sense of Cisinski-D{\\'e}glise \\cite{mixedmotives}, and have transfers if"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4117","kind":"arxiv","version":3},"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"}