{"paper":{"title":"Very simple 2-adic representations and hyperelliptic jacobians","license":"","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Yuri G. Zarhin","submitted_at":"2001-09-03T14:27:39Z","abstract_excerpt":"Let $K$ be a number field, $n>4$ an integer, $f(x)$ an irreducible polynomial over $K$ of degree $n$, whose Galois group is either the full symmetric group $S_n$ or the alternating group $A_n$. Suppose $C:y^2=f(x)$ is the corresponding hyperelliptic curve and $J$ its jacobian defined over $K$. For each prime $\\ell$ we write $V_{\\ell}(J)$ for the $Q_{\\ell}$-Tate module of $J$ and $e_{\\ell}$ for the Riemann form on $V_{\\ell}(J)$ attached to the theta divisor. (Here $Q_{\\ell}$ is the field of $\\ell$-adic numbers.)\n We write $sp(V_{\\ell}(J))$ for the $Q_{\\ell}$-Lie algebra of the symplectic group "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0109014","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"}