{"paper":{"title":"Relative Cartier divisors and K-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Charles Weibel, Vivek Sadhu","submitted_at":"2016-04-20T13:34:29Z","abstract_excerpt":"We study the relative Picard group $Pic(f)$ of a map $f:X\\to S$ of schemes. If $f$ is faithful affine, it is the relative Cartier divisor group $I(f)$. The relative group $K_0(f)$ has a $\\gamma$-filtration, and $Pic(f)$ is the top quotient for the $\\gamma$-filtration. When $f$ is induced by a ring homomorphism $A\\to B$, we show that the relative \"nil\" groups $NPic(f)$ and $NK_n(f)$ are continuous $W(A)$-modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05951","kind":"arxiv","version":1},"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"}