{"paper":{"title":"A Hasse principle for the higher Chow groups of curves over a global field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Toshiro Hiranouchi","submitted_at":"2025-07-30T01:26:23Z","abstract_excerpt":"We study the higher Chow group $CH^2(X,1)$ of a smooth projective curve $X$ over a global field $F$, focusing on the kernel $V(X)$ of the push-forward map $CH^2(X,1) \\to CH^1(F,1) = F^\\times$. Our main purpose is to investigate the structure of the torsion subgroup of $V(X)$ and its relation to the arithmetic of the curve. Using Bloch's exact sequence together with a Hasse principle for Galois cohomology arising from mod-$l$ Galois representations, we show that the mod-$l$ quotient $V(X)/lV(X)$ is governed by the mod-$l$ Galois representation on the $l$-torsion subgroup $J[l]$ of the Jacobian "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.22319","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.22319/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}