{"paper":{"title":"Cohomology with integral coefficients of stacks of shtukas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Cong Xue","submitted_at":"2020-01-16T14:06:05Z","abstract_excerpt":"We construct the cohomology groups with compact support of stacks of shtukas with $\\mathbb Z_{\\ell}$-coefficients. We construct the cuspidal cohomology groups and prove that they are $\\mathbb Z_{\\ell}$-modules of finite type. We prove that the cohomology groups are modules of finite type over a Hecke algebra with $\\mathbb Z_{\\ell}$-coefficients.\n  As an application, we prove that the cuspidal cohomology groups with $\\mathbb Q_{\\ell}$-coefficients are equal to the Hecke-finite cohomology groups with $\\mathbb Q_{\\ell}$-coefficients defined by V. Lafforgue.\n  We also state the Eichler-Shimura rel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.05805","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2001.05805/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"}