{"paper":{"title":"On equivariant Serre problem for principal bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Arijit Dey, Indranil Biswas, Mainak Poddar","submitted_at":"2017-07-20T17:30:19Z","abstract_excerpt":"Let $E_G$ be a $\\Gamma$--equivariant algebraic principal $G$--bundle over a normal complex affine variety $X$ equipped with an action of $\\Gamma$, where $G$ and $\\Gamma$ are complex linear algebraic groups. Suppose $X$ is contractible as a topological $\\Gamma$--space with a dense orbit, and $x_0 \\in X$ is a $\\Gamma$--fixed point. We show that if $\\Gamma$ is reductive, then $E_G$ admits a $\\Gamma$--equivariant isomorphism with the product principal $G$--bundle $X \\times_{\\rho} E_G(x_0)$, where $\\rho\\,:\\, \\Gamma \\, \\longrightarrow\\, G$ is a homomorphism between algebraic groups. As a consequence"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06623","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"}