{"paper":{"title":"On Greenberg's generalized conjecture for imaginary quartic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Naoya Takahashi","submitted_at":"2020-01-31T11:03:29Z","abstract_excerpt":"For an algebraic number field $K$ and a prime number $p$, let $\\widetilde{K}/K$ be the maximal multiple $\\mathbb{Z}_p$-extension. Greenberg's generalized conjecture (GGC) predicts that the Galois group of the maximal unramified abelian pro-$p$ extension of $\\widetilde{K}$ is pseudo-null over the completed group ring $\\mathbb{Z}_p[\\![\\mathop{\\mathrm{Gal}}\\nolimits(\\widetilde{K}/K)]\\!]$. We show that GGC holds for some imaginary quartic fields containing imaginary quadratic fields and some prime numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.11768","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/2001.11768/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"}