{"paper":{"title":"Hilbert-90 quotient maps, torsion defects, and symmetric monodromy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Henry Shin","submitted_at":"2026-05-24T23:12:06Z","abstract_excerpt":"Let $\\tau(z)=-1-z^{-1}$. We study the reduced rational maps $h_d:\\mathbb{P}^1\\to\\mathbb{P}^1$ obtained by cancelling common factors in $H_d^{\\rm raw}(z)=z^d(\\tau(z)^d-1)/(z^d-1)$. These maps arise by Hilbert-90 descent from the trace-zero maps $X^{dq}-X^d$ on $\\ker\\operatorname{Tr}_{\\mathbb{F}_{q^3}/\\mathbb{F}_q}$, but the principal object is the resulting $\\tau$-equivariant quotient-map family; nonconstant separable members are viewed as covers.\n  We prove that cancellation is exactly a torsion-defect phenomenon. If $\\ell(-)$ denotes scheme-theoretic length and $\\boldsymbol{\\mu}_d=\\ker([d]:\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25291","kind":"arxiv","version":1},"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/2605.25291/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"}