{"paper":{"title":"On the Conservativity of the Functor Assigning to a Motivic Spectrum its Motive","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT"],"primary_cat":"math.KT","authors_text":"Tom Bachmann","submitted_at":"2015-06-24T14:18:56Z","abstract_excerpt":"Given a 0-connective motivic spectrum $E \\in SH(k)$ over a perfect field k, we determine $h_0$ of the associated motive $M E \\in DM(k)$ in terms of $\\pi_0 (E)$. Using this we show that if k has finite 2-\\'etale cohomological dimension, then the functor M is conservative when restricted to the subcategory of compact spectra, and induces an injection on Picard groups. We extend the conservativity result to fields of finite virtual 2-\\'etale cohomological dimension by considering what we call \"real motives\".\n  As a by-product we reprove a variant of a rigidity Theorem of R\\\"ondings-{\\O}stv{\\ae}r."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07375","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"}