{"paper":{"title":"The Fundamental Theorem of Tropical Differential Algebraic Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Cristhian Garay, Fuensanta Aroca, Zeinab Toghani","submitted_at":"2015-10-04T23:55:03Z","abstract_excerpt":"Let $I$ be an ideal of the ring of Laurent polynomials $K[x_1^{\\pm1},\\ldots,x_n^{\\pm1}]$ with coefficients in a real-valued field $(K,v)$. The fundamental theorem of tropical algebraic geometry states the equality $\\text{trop}(V(I))=V(\\text{trop}(I))$ between the tropicalization $\\text{trop}(V(I))$ of the closed subscheme $V(I)\\subset (K^*)^n$ and the tropical variety $V(\\text{trop}(I))$ associated to the tropicalization of the ideal $\\text{trop}(I)$.\n  In this work we prove an analogous result for a differential ideal $G$ of the ring of differential polynomials $K[[t]]\\{x_1,\\ldots,x_n\\}$, whe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01000","kind":"arxiv","version":3},"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"}