{"paper":{"title":"Big de Rham-Witt cohomology: basic results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.KT"],"primary_cat":"math.NT","authors_text":"Andre Chatzistamatiou","submitted_at":"2012-11-26T16:13:38Z","abstract_excerpt":"Let $X$ be a smooth projective $R$-scheme, where $R$ is a smooth $\\Z$-algebra. As constructed by Hesselholt, we have the absolute big de Rham-Witt complex $\\W\\Omega^*_X$ of $X$ at our disposal. There is also a relative version $\\W\\Omega^*_{X/R}$ with $\\W(R)$-linear differential. In this paper we study the hypercohomology of the relative (big) de Rham-Witt complex after truncation with finite truncation sets $S$. We show that it is a projective $\\W_S(R)$-module, provided that the de Rham cohomology is a flat $R$-module. In addition, we establish a Poincar\\'e duality theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6006","kind":"arxiv","version":4},"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"}