{"paper":{"title":"Motivic bivariant characteristic classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Shoji Yokura","submitted_at":"2010-05-07T02:46:01Z","abstract_excerpt":"The relative Grothendieck group $K_0(\\m V/X)$ is the free abelian group generated by the isomorphism classes of complex algebraic varieties over $X$ modulo the \"scissor relation\". The motivic Hirzebruch class ${T_y}_*: K_0(\\m V /X) \\to H_*^{BM}(X) \\otimes \\bQ[y]$ is a unique natural transformation satisfying that for a nonsingular variety $X$ the value ${T_y}_*([X \\xrightarrow {\\op {id}_X} X])$ of the isomorphism class of the identity $X \\xrightarrow {id_X} X$ is the Poincar\\'e dual of the Hirzebruch cohomology class of the tangent bundle $TX$. It \"unifies\" the well-known three characteristic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1124","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"}