{"paper":{"title":"Relative Mather discrepancy on arc spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Tommaso de Fernex, Zach Mere","submitted_at":"2025-08-17T16:10:40Z","abstract_excerpt":"Given any generically \\'etale morphism of varieties $f \\colon X \\to Y$, we define the relative Mather discrepancy function on the arc space $X_\\infty$ of the domain and show that this function computes the dimension of the kernel of the differential map of the induced morphism on arc spaces $f_\\infty \\colon X_\\infty \\to Y_\\infty$. We relate this result to the change-of-variable formula in motivic integration. We introduce the notion of $\\widehat K$-equivalence, which agrees with $K$-equivalence for smooth varieties, and prove that $\\widehat K$-equivalent varieties of arbitrary characteristic d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.12420","kind":"arxiv","version":4},"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/2508.12420/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"}