{"paper":{"title":"On the rapid decay homology of F.Pham","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AP","math.CV"],"primary_cat":"math.CA","authors_text":"Saiei-Jaeyeong Matsubara-Heo","submitted_at":"2017-05-17T08:53:42Z","abstract_excerpt":"In \\cite{hien}, M. Hien introduced rapid decay homology group $\\Homo^{rd}_{*}(U, (\\nabla, E))$ associated to an irregular connection $(\\nabla, E)$ on a smooth complex affine variety $U$, and showed that it is the dual group of the algebraic de Rham cohomology group $\\Homo^*_{dR}(U,(\\nabla^{\\vee}, E^{\\vee}))$. On the other hand, F. Pham has already introduced his version of rapid decay homology when $(\\nabla, E)$ is the so-called elementary irregular connection (\\cite{Sab}) in \\cite{Pham}. In this report, we will state a comparison theorem of these homology groups and give an outline of its pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06052","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":""},"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"}