{"paper":{"title":"Artin-Mazur heights and Yobuko heights of proper log smooth schemes of Cartier type, and Hodge-Witt decompositions and Chow groups of quasi-$F$-split threefolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Yukiyoshi Nakkajima","submitted_at":"2019-02-01T05:04:40Z","abstract_excerpt":"In this article we prove a fundamental inequality between Artin-Mazur heights and Yobuko heights of certain proper log smooth schemes of Cartier type over a fine log scheme whose underlying scheme is the spectrum of a perfect field $\\kappa$ of characteristic $p>0$. We also prove that the cohomologies of Witt-sheaves of them are finitely generated ${\\cal W}(\\kappa)$-modules if the Yobuko heights of them are finite. As an application, we prove that the $p$-primary torsion parts of the Chow groups of codimension $2$ of proper smooth threefolds over $\\kappa$ is of finite cotype if the Yobuko heigh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00185","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"}