{"paper":{"title":"An algorithm to compute Selmer groups via resolutions by permutations modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.NT","math.RT"],"primary_cat":"cs.SC","authors_text":"CANARI, Fabrice Etienne (UB, IMB)","submitted_at":"2025-04-18T06:57:38Z","abstract_excerpt":"Given a number field with absolute Galois group $\\mathcal{G}$, a finite Galois module $M$, and a Selmer system $\\mathcal{L}$, this article gives a method to compute Sel$_\\mathcal{L}$, the Selmer group of $M$ attached to $\\mathcal{L}$. First we describe an algorithm to obtain a resolution of $M$ where the morphisms are given by Hecke operators. Then we construct another group $H^1_S(\\mathcal{G}, M)$ and we prove, using the properties of Hecke operators, that $H^1_S(\\mathcal{G}, M)$ is a Selmer group containing Sel$_\\mathcal{L}$. Then, we discuss the time complexity of this method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.13506","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/2504.13506/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"}