{"paper":{"title":"On the formal arc space of a reductive monoid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Alexis Bouthier, Ngo Bao Chau, Yiannis Sakellaridis","submitted_at":"2014-12-18T23:11:58Z","abstract_excerpt":"Let $X$ be a scheme of finite type over a finite field $k$, and let $\\mathcal L X$ denote its arc space; in particular, $\\mathcal L X(k) = X(k[[t]])$. Using the theory of Grinberg, Kazhdan, and Drinfeld on the finite-dimensionality of singularities of $\\mathcal L X$ in the neighborhood of non-degenerate arcs, we show that a canonical \"basic function\" can be defined on the non-degenerate locus of $\\mathcal L X(k)$, which corresponds to the trace of Frobenius on the stalks of the intersection complex of any finite-dimensional model. We then proceed to compute this function when $X$ is an affine "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6174","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":""},"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"}