{"paper":{"title":"Automorphy of mod 2 Galois representations associated to the quintic Dwork family and reciprocity of some quintic trinomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Nobuo Tsuzuki, Takuya Yamauchi","submitted_at":"2020-08-22T15:14:27Z","abstract_excerpt":"In this paper, we determine mod $2$ Galois representations $\\bar{\\rho}_{\\psi,2}:G_K:={\\rm Gal}(\\bar{K}/K)\\longrightarrow {\\rm GSp}_4(\\mathbb{F}_2)$ associated to the mirror motives of rank 4 with pure weight 3 coming from the Dwork quintic family $$X^5_0+X^5_1+X^5_2+X^5_3+X^5_4-5\\psi X_0X_1X_2X_3X_4=0,\\ \\psi\\in K$$ defined over a number field $K$ under the irreducibility condition of the quintic trinomial $f_\\psi$ below. Applying this result, when $K=F$ is a totally real field, for some at most qaudratic totally real extension $M/F$, we prove that $\\bar{\\rho}_{\\psi,2}|_{G_M}$ is associated to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.09852","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2008.09852/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"}