{"paper":{"title":"Milnor $K$-groups and function fields of hypersurfaces in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Stephen Scully","submitted_at":"2012-02-29T17:01:45Z","abstract_excerpt":"Let $X$ be an integral affine or projective hypersurface over a field $F$ of characteristic $p>0$, and let $F(X)$ denote its function field. In a recent article, Dolphin and Hoffmann obtained an explicit description of the kernel of the natural restriction homomorphism between the rings of absolute K\\\"{a}hler differentials of $F$ and $F(X)$, respectively. In this note, we examine the possibility of deriving an analogous result for mod-$p$ Milnor $K$-theory using the Bloch-Gabber-Kato theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6604","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"}