{"paper":{"title":"Hurwitz spaces, Nichols algebras, and Igusa zeta functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT","math.QA"],"primary_cat":"math.AG","authors_text":"Kevin Chang","submitted_at":"2023-06-18T00:46:33Z","abstract_excerpt":"By constructing new quasimap compactifications of Hurwitz spaces of degrees 4 and 5, we establish a new connection between arithmetic statistics, quantum algebra, and geometry and answer a question of Ellenberg-Tran-Westerland and Kapranov-Schechtman. It follows from the geometry of our compactifications and a comparison theorem of Kapranov-Schechtman that we can precisely relate the following 3 quantities: (1) counts of $\\mathbb{F}_q[t]$-algebras of degrees 3, 4, and 5 (2) the ``invariant'' part of the cohomology of certain special Nichols algebras (3) Igusa local zeta functions for certain p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.10446","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.10446/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"}