{"paper":{"title":"On the continuity of the geometric side of the trace formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Erez Lapid, Tobias Finis","submitted_at":"2015-12-29T18:54:16Z","abstract_excerpt":"We extend the geometric side of Arthur's non-invariant trace formula for a reductive group $G$ defined over $\\mathbb{Q}$ continuously to a natural space $\\mathcal{C}(G(\\mathbb{A}^1))$ of test functions which are not necessarily compactly supported. The analogous result for the spectral side was obtained in [MR2811597]. The geometric side is decomposed according to the following equivalence relation on $G(\\mathbb{Q})$: $\\gamma_1\\sim\\gamma_2$ if $\\gamma_1$ and $\\gamma_2$ are conjugate in $G(\\bar{\\mathbb{Q}})$ and their semisimple parts are conjugate in $G(\\mathbb{Q})$. All terms in the resulting"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08753","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":""},"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"}