{"paper":{"title":"Comparing motives of smooth algebraic varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.KT"],"primary_cat":"math.AG","authors_text":"Grigory Garkusha","submitted_at":"2017-09-26T15:50:35Z","abstract_excerpt":"Given a perfect field of exponential characteristic $e$ and a functor $f:\\mathcal A\\to\\mathcal B$ between symmetric monoidal strict $V$-categories of correspondences satisfying the cancellation property such that the induced morphisms of complexes of Nisnevich sheaves\n  $$f_*:\\mathbb Z_{\\mathcal A}(q)[1/e]\\to\\mathbb Z_{\\mathcal B}(q)[1/e],\\quad q\\geq 0,$$ are quasi-isomorphisms, it is proved that for every $k$-smooth algebraic variety $X$ the morphisms of twisted motives of $X$ with $\\mathbb Z[1/e]$-coefficients\n  $$M_{\\mathcal A}(X)(q)\\otimes\\mathbb Z[1/e]\\to M_{\\mathcal B}(X)(q)\\otimes\\mathb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09097","kind":"arxiv","version":2},"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"}