{"paper":{"title":"Ordinary and almost ordinary Prym varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Ekin Ozman, Rachel Pries","submitted_at":"2015-02-20T18:09:11Z","abstract_excerpt":"We study the $p$-rank stratification of the moduli space of Prym varieties in characteristic $p > 0$. For arbitrary primes $p$ and $\\ell$ with $\\ell \\not = p$ and integers $g \\geq 3$ and $0 \\leq f \\leq g$, the first theorem generalizes a result of Nakajima by proving that the Prym varieties of all the unramified ${\\mathbb Z}/\\ell$-covers of a generic curve $X$ of genus $g$ and $p$-rank $f$ are ordinary. Furthermore, when $p \\geq 5$ and $\\ell = 2$, the second theorem implies that there exists a curve of genus $g$ and $p$-rank $f$ having an unramified double cover whose Prym has $p$-rank $f'$ fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05959","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":""},"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"}