{"paper":{"title":"Generalized Picard-Vessiot extensions and differential Galois cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Anand Pillay, Zoe Chatzidakis","submitted_at":"2017-02-07T11:45:44Z","abstract_excerpt":"In an earlier paper it was proved that if a differential field $(K,\\delta)$ is algebraically closed and closed under Picard-Vessiot extensions then every differential algebraic principal homogeneous space over K for a linear differential algebraic group G over K has a K-rational point (in fact if and only if). This paper explores whether and if so, how, this can be extended to (a) several derivations, (b) one automorphism. Under a natural notion of \"generalized Picard-Vessiot extension\" (in the case of several derivations), we give a counterexample. We also have a counterexample in the case of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01969","kind":"arxiv","version":2},"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"}