{"paper":{"title":"Lifting Galois sections along torsors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Jakob Stix, Michel Emsalem, Niels Borne","submitted_at":"2013-01-18T16:50:07Z","abstract_excerpt":"The cuspidalization conjecture, which is a consequence of Grothendieck's section conjecture, asserts that for any smooth hyperbolic curve $X$ over a finitely generated field $k$ of characteristic $0$ and any non empty Zariski open $U \\subset X$, every section of $\\pi _1 (X, \\bar x) \\to \\mathrm{Gal}_k$ lifts to a section of $\\pi _1 (U,\\bar x) \\to \\mathrm{Gal}_k$. We consider in this article the problem of lifting Galois sections to the intermediate quotient $ \\pi_1^{cc}(U)$ introduced by Mochizuki. We show that when $k = \\mathbb Q$ and $D=X\\setminus U$ is an union of torsion sub-packets every G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4429","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"}