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We ask whether Y admits a G_0 -equivariant k_0 -model Y_0 of Y.\n  We assume that Y admits a G_q -equivariant k_0 -model Y_q, where G_q is an inner form of G_0. We give a Galois-cohomological criterion for the existence of a G_0 -equivariant k_0 -model Y_0 of Y. We apply this criterion to spherical homogeneous varieties Y=G/H."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1804.08475","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-04-23T14:39:40Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"8119233ca7812608c1113d24a21029795ed6c1b52823a5d0cf4f8495da611f3c","abstract_canon_sha256":"f584a7af637e5661a794303fe9c5eecc244b21326d7ca023a9a70ea6906151c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:07.429652Z","signature_b64":"tllMMNnpd81vz/YA7Z3GzZaVGKsa1dWc9H1hRlQKwJdhW4fnvid1bqsETeV3758IRjarLZ5Hjrqulf5K4IXUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"009cac8adef6b98a5d57becb800574b9b7d4d3066470fecc26c56accfa727297","last_reissued_at":"2026-05-18T00:16:07.428956Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:07.428956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of equivariant models of G-varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.GR","authors_text":"Mikhail Borovoi","submitted_at":"2018-04-23T14:39:40Z","abstract_excerpt":"Let k_0 be a field of characteristic 0, and let k be a fixed algebraic closure of k_0. Let G be an algebraic k-group, and let Y be a G-variety over k. Let G_0 be a k_0 -model (k_0 -form) of G. We ask whether Y admits a G_0 -equivariant k_0 -model Y_0 of Y.\n  We assume that Y admits a G_q -equivariant k_0 -model Y_q, where G_q is an inner form of G_0. We give a Galois-cohomological criterion for the existence of a G_0 -equivariant k_0 -model Y_0 of Y. 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