{"paper":{"title":"Determinants of Subquotients of Galois Representations Associated to Abelian Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Dmitry Vaintrob, Eric Larson","submitted_at":"2011-10-03T02:22:34Z","abstract_excerpt":"Given an abelian variety $A$ of dimension $g$ over a number field $K$, and a prime $\\ell$, the $\\ell^n$-torsion points of $A$ give rise to a representation $\\rho_{A, \\ell^n} : \\gal(\\bar{K} / K) \\to \\gl_{2g}(\\zz/\\ell^n\\zz)$. In particular, we get a mod-$\\ell$ representation $\\rho_{A, \\ell} : \\gal(\\bar{K} / K) \\to \\gl_{2g}(\\ff_\\ell)$and an $\\ell$-adic representation $\\rho_{A, \\ell} : \\gal(\\bar{K} / K) \\to \\gl_{2g}(\\zz_\\ell)$.\n  In this paper, we describe the possible determinants of subrepresentations (or more generally, subquotients) of these two representation for $\\ell$ a prime number, as $A$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0255","kind":"arxiv","version":4},"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"}