{"paper":{"title":"Blocks for mod $p$ representations of $GL_2(Q_p)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Vytautas Paskunas","submitted_at":"2011-04-29T11:44:14Z","abstract_excerpt":"Let $\\pi_1$ and $\\pi_2$ be absolutely irreducible smooth representations of $G=GL_2(Q_p)$ with a central character, defined over a finite field of characteristic $p$. We show that if there exists a non-split extension between $\\pi_1$ and $\\pi_2$ then they both appear as subquotients of the reduction modulo $p$ of a unit ball in a crystalline Banach space representation of $G$. The results of Berger-Breuil describe such reductions and allow us to organize the irreducible representation into blocks. The result is new for $p=2$, the proof, which works for all $p$, is new."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5602","kind":"arxiv","version":2},"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"}