{"paper":{"title":"Extension of functors for algebras of formal deformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ana Rita Martins, David Raimundo, Teresa Monteiro Fernandes","submitted_at":"2012-01-02T21:21:51Z","abstract_excerpt":"Suppose we are given complex manifolds $X$ and $Y$ together with substacks $\\mathcal{S}$ and $\\mathcal{S}'$ of modules over algebras of formal deformation $\\mathcal{A}$ on $X$ and $\\mathcal{A}'$ on $Y$, respectively. Suppose also we are given a functor $\\Phi$ from the category of open subsets of $X$ to the category of open subsets of $Y$ together with a functor $F$ of prestacks from $\\mathcal{S}$ to $\\mathcal{S}'\\circ\\Phi$. Then we give conditions for the existence of a canonical functor, extension of $F$ to the category of coherent ${\\sha}$-modules such that the cohomology associated to the a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0536","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"}