{"paper":{"title":"About top-degree $L^2$- and $L^{2,\\mathrm{loc}}$-Dolbeault cohomologies of complex spaces with pseudoconvex boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG"],"primary_cat":"math.CV","authors_text":"Martin Sera","submitted_at":"2026-05-26T08:41:47Z","abstract_excerpt":"Let $X$ be a complex space of pure-dimension $n$. For a pseudoconvex relatively compact domain in $X$ with $\\mathscr{C}^3$-smooth boundary and embedded in a domain of the complex number space, we prove that the $L^2$- and $L^{2,\\mathrm{loc}}$-Dolbeault $(n,q)$-cohomology groups are vanishing for $q>0$. Thereby, we include the case that the forms have values in a Nakano semi-positive holomorphic vector bundle. Using this local vanishing theorem, we also prove the equivalence of the $L^2$- and $L^{2,\\mathrm{loc}}$-Dolbeault $(n,q)$-cohomology groups of domains $\\Omega=\\{\\rho<0\\}$ in $X$ which ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26700","kind":"arxiv","version":1},"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/2605.26700/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"}