{"paper":{"title":"Strictly homotopy invariance of Nisnevich sheaves with GW-transfers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrei Druzhinin","submitted_at":"2017-09-18T08:09:46Z","abstract_excerpt":"The strictly homotopy invariance of the associated Nisnevish sheave $\\widetilde{\\mathcal F}_{Nis}$ of a homotopy invariant presheave $\\mathcal F$ with GW-transfers (or Witt-transfers) on the category of smooth varieties over a prefect field $k$, $char\\,k \\neq 2$, is proved, i.e. the isomorphism $$H^i_{Nis}(\\mathbb A^1\\times X,\\widetilde{\\mathcal F}_{Nis})\\simeq H^i_{Nis}(X,\\widetilde{\\mathcal F}_{Nis})$$ for any $X\\in Sm_k$ is obtained. This theorem is necessary for the construction of the triangulated category of GW-motives $\\mathbf{DM}^{GW}(k)$ and Witt-motives $\\mathbf{DM}^W(k)$ by the Voev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05805","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"}