{"paper":{"title":"Estimates on volumes of homogeneous polynomial spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.LO"],"primary_cat":"math.AG","authors_text":"Ita\\\"i Ben Yaacov (ICJ)","submitted_at":"2018-01-22T08:52:29Z","abstract_excerpt":"In this paper we develop the \"local part\" of our local/global approach to globally valued fields (GVFs). The \"global part\", which relies on these results, is developed in a subsequent paper.We study virtual divisors on projective varieties defined over a valued field $K$, as well as sub-valuations on polynomial rings over $K$ (analogous to homogeneous polynomial ideals). We prove a Nullstellensatz-style duality between projective varieties equipped with virtual divisors (analogous to projective varieties over a plain field) and certain sub-valuations on polynomial rings over $K$ (analogous to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06994","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"}