{"paper":{"title":"$l$-adic \\'etale cohomology of Shimura varieties of Hodge type with non-trivial coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Paul Hamacher, Wansu Kim","submitted_at":"2017-11-20T02:32:59Z","abstract_excerpt":"Let $(\\mathsf{G},\\mathsf{X})$ be a Shimura datum of Hodge type. Let $p$ be an odd prime such that $\\mathsf{G}_{\\mathbb{Q}_p}$ splits after a tamely ramified extension and $p\\nmid |\\pi_1(\\mathsf{G}^{\\rm der})|$. Under some mild additional assumptions that are satisfied if the associated Shimura variety is proper and $\\mathsf{G}_{\\mathbb{Q}_p}$ is either unramified or residually split, we prove the generalisation of Mantovan's formula for the $l$-adic cohomology of the associated Shimura variety. On the way we derive some new results about the geometry of the Newton stratification of the reducti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07123","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"}