{"paper":{"title":"Line Bundles on The First Drinfeld Covering","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.RT","authors_text":"James Taylor","submitted_at":"2023-07-24T17:14:44Z","abstract_excerpt":"Let $\\Omega^d$ be the $d$-dimensional Drinfeld symmetric space for a finite extension $F$ of $\\mathbb{Q}_p$. Let $\\Sigma^1$ be a geometrically connected component of the first Drinfeld covering of $\\Omega^d$ and let $\\mathbb{F}$ be the residue field of the unique degree $d+1$ unramified extension of $F$. We show that the natural homomorphism determined by the second Drinfeld covering from the group of characters of $(\\mathbb{F}, +)$ to $\\text{Pic}(\\Sigma^1)[p]$ is injective. In particular, $\\text{Pic}(\\Sigma^1)[p] \\neq 0$. We also show that all vector bundles on $\\Omega^1$ are trivial, which e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.12942","kind":"arxiv","version":3},"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/2307.12942/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"}