{"paper":{"title":"Motivic fundamental groups of CM elliptic curves and geometry of Bianchi hyperbolic threefolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Nikolay Malkin","submitted_at":"2020-10-14T16:54:10Z","abstract_excerpt":"In this paper we describe a connection between realizations of the action of the motivic Galois group on the motivic fundamental groups of Gaussian and Eisenstein elliptic curves punctured at the $\\mathfrak{p}$-torsion points, $\\pi_1^{\\rm Mot}(E-E[\\mathfrak{p}],v_0)$, and the geometry of the Bianchi hyperbolic threefolds $\\Gamma_1(\\mathfrak{p})\\setminus\\mathbb{H}^3$, where $\\Gamma_1(\\mathfrak{p})$ is a congruence subgroup of ${\\rm GL}_2({\\rm End}(E))$. The first instance of such a connection was found by A.Goncharov (arXiv:math/0510310).\n  In particular, we study the Hodge realization of the i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.07238","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/2010.07238/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"}