{"paper":{"title":"Sur le comptage des fibr\\'es de Hitchin nilpotents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"G\\'erard Laumon, Pierre-Henri Chaudouard","submitted_at":"2013-07-27T15:59:29Z","abstract_excerpt":"This paper is concerned with two problems. One is to count Hitchin bundles on a projective curve and the other is to get an explicit formula for the nilpotent part of the Arthur-Selberg trace formula for a simple test function. The fact that the two problems are in fact related has been noticed in a previous paper. We expand the nilpotent part of the Arthur-Selberg trace formula in a sum of adelic integrals indexed by nilpotent orbits. For \"regular by blocks\" orbits, we get an explicit formula for these integrals in terms of the zeta function of the curve."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7273","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"}