{"paper":{"title":"Around the Thom-Sebastiani theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Luc Illusie","submitted_at":"2016-04-24T09:32:12Z","abstract_excerpt":"For germs of holomorphic functions $f : (\\mathbf{C}^{m+1},0) \\to (\\mathbf{C},0)$, $g : (\\mathbf{C}^{n+1},0) \\to (\\mathbf{C},0)$ having an isolated critical point at 0 with value 0, the classical Thom-Sebastiani theorem describes the vanishing cycles group $\\Phi^{m+n+1}(f \\oplus g)$ (and its monodromy) as a tensor product $\\Phi^m(f) \\otimes \\Phi^n(g)$, where $(f \\oplus g)(x,y) = f(x) + g(y), x = (x_0,...,x_m), y = (y_0,...,y_n)$. We prove algebraic variants and generalizations of this result in \\'etale cohomology over fields of any characteristic, where the tensor product is replaced by a certa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07004","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"}