{"paper":{"title":"Local Tropicalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dmitry Stepanov, Patrick Popescu-Pampu","submitted_at":"2012-04-27T09:21:26Z","abstract_excerpt":"In this paper we propose a general functorial definition of the operation of \\emph{local tropicalization} in commutative algebra. Let $R$ be a commutative ring, $\\Gamma$ a finitely generated subsemigroup of a lattice, $\\gamma : \\Gamma \\rightarrow R/ R^*$ a morphism of semigroups, and $\\V(R)$ the topological space of valuations on $R$ taking values in $\\R \\cup \\infty$. Then we may \\emph{tropicalize} with respect to $\\gamma$ any subset $\\W$ of the space of valuations $\\V(R)$. By definition, we get a subset of a rational polyhedral cone canonically associated to $\\Gamma$, enriched with strata at "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6154","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"}