{"paper":{"title":"A PEL-type Igusa Stack and the $p$-adic Geometry of Shimura Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Mingjia Zhang","submitted_at":"2023-09-10T22:03:58Z","abstract_excerpt":"Let $(G,X)$ be a PEL-Shimura datum of type AC in Kottwitz's classification. Assume $G_{\\mathbf{Q}_p}$ is unramified. We show that the good reduction locus of the infinite $p$-level Shimura variety attached to this datum, considered as a diamond, can be described as the fiber product of a certain v-stack (which we call ``Igusa stack\") with a Schubert cell of the corresponding $B_{dR}^+$-affine Grassmannian, over the stack of $G_{\\mathbf{Q}_p}$-torsors on the Fargues-Fontaine curve. We also construct a minimal compactification of the Igusa stack and show that this fiber product structure extends"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.05152","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/2309.05152/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"}