{"paper":{"title":"Reconstruction of Function Fields from their pro-l abelian divisorial Inertia","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Florian Pop","submitted_at":"2018-10-10T22:40:02Z","abstract_excerpt":"Let $\\Pi^c_K\\to\\Pi_K$ be the maximal pro-$\\ell$ abelian-by-central, respectively abelian, Galois groups of a function field $K|k$ with $k$ algebraically closed and ${\\rm char}\\neq\\ell$. We show that $K|k$ can be functorially reconstructed by group theoretical recipes from $\\Pi^c_K$ endowed with the set of divisorial inertia ${\\rm Inrdiv}(K)\\subset\\Pi_K$. As applications, one has: (i) A group theoretical recipe to reconstruct $K|k$ from $\\Pi^c_K$, provided either ${\\rm Tr.deg}(K|k)>{\\rm dim}(k)+1$ or ${\\rm tr.deg}(K|k) >{\\rm dim}(k)>1$, where ${\\rm dim}(k)$ is the Kronecker dimension; (ii) An a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04768","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"}