{"paper":{"title":"The intersection matrices of $X_0(p^r)$ and some applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chitrabhanu Chaudhuri, Debargha Banerjee, Priyanka Majumder","submitted_at":"2022-10-17T09:02:44Z","abstract_excerpt":"We compute intersection matrices for modular curves of the form $X_0(p^r)$ with $r \\in \\{3,4\\}$ and as an application, we compute an asymptotic expression for the Arakelov self-intersection number of the relative dualizing sheaf of Edixhoven's minimal regular model for the modular curve $X_0(p^r)$ over $\\qq$ with $r$ as above. This computation will be useful to understand an effective version of the Bogolomov conjecture for the stable models of modular curves $X_0(p^r)$ with $r \\in \\{3,4\\}$ and obtain a bound on the stable Faltings height for those curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.08866","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/2210.08866/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"}