{"paper":{"title":"Fixed points and homology of superelliptic Jacobians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Chia-Fu Yu, Haining Wang, Jiangwei Xue","submitted_at":"2013-09-02T03:22:08Z","abstract_excerpt":"Let $\\eta: C_{f,N}\\to \\mathbb{P}^1$ be a cyclic cover of $\\mathbb{P}^1$ of degree $N$ which is totally and tamely ramified for all the ramification points. We determine the group of fixed points of the cyclic group $\\mathbf{mu}_N\\cong \\mathbb{Z}/N\\mathbb{Z}$ acting on the Jacobian $J_N:=\\Jac(C_{f,N})$. For each $\\ell$ distinct from the characteristic of the base field, the Tate module $T_\\ell J_N$ is shown to be a free module over the ring $\\mathbb{Z}_\\ell[T]/(\\sum_{i=0}^{N-1}T^i)$. We also calculate the degree of the induced polarization on the new part $J_N^{new}$ of the Jacobian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0295","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"}