{"paper":{"title":"An explicit geometric Langlands correspondence for the projective line minus four points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Niels uit de Bos","submitted_at":"2019-06-07T17:01:36Z","abstract_excerpt":"This article deals with the tamely ramified geometric Langlands correspondence for GL_2 on $\\mathbf{P}_{\\mathbf{F}_q}^1$, where $q$ is a prime power, with tame ramification at four distinct points $D = \\{\\infty, 0,1, t\\} \\subset \\mathbf{P}^1(\\mathbf{F}_q)$. We describe in an explicit way (1) the action of the Hecke operators on a basis of the cusp forms, which consists of $q$ elements; and (2) the correspondence that assigns to a pure irreducible rank 2 local system $E$ on $\\mathbf{P}^1 \\setminus D$ with unipotent monodromy its Hecke eigensheaf on the moduli space of rank 2 parabolic vector bu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03240","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":""},"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"}