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We establish a unified criterion determining when the base change homomorphism $\\pi(\\mathcal{C}_{X_K},x_K)\\rightarrow \\pi(\\mathcal{C}_X,x)_K$ is faithfully flat or an isomorphism. As applications, we recover and generalize base c"},"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":"2602.11110","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-02-11T18:23:58Z","cross_cats_sorted":[],"title_canon_sha256":"a9b675b08f803df561e4babeede9f6791aa04402065a37edc99177a76bf0180e","abstract_canon_sha256":"1384177e4a07b5b716287019f35053a121dada6354e512de27e51478e6d6411d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T01:10:59.389594Z","signature_b64":"gQ13M+9r6tduZNmeQauHqYWItfr6nMx3iUu0L4N9JpkqvFcEgUQkRCQ2JMYRO5sxnboDOCl8XlgTz5rrjC3jAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79bf0fe22a969a1aa2b0cf458df9fecedec59c58d40aec34ed28017ff4deb44f","last_reissued_at":"2026-06-10T01:10:59.388587Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T01:10:59.388587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Base Change Of Fundamental Group Schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Lingguang Li, Niantao Tian","submitted_at":"2026-02-11T18:23:58Z","abstract_excerpt":"Let $k$ be a field, $K/k$ a field extension, $X$ a connected scheme proper over $k$, $x_K\\in X_K(K)$ lying over $x\\in X(k)$, $\\mathcal{C}_X$ and $\\mathcal{C}_{X_K}$ the Tannakian categories whose objects consist of vector bundles on $X$ and $X_K$ respectively, $\\pi(\\mathcal{C}_X,x)$ and $\\pi(\\mathcal{C}_{X_K},x_K)$ the corresponding Tannaka group schemes respectively. We establish a unified criterion determining when the base change homomorphism $\\pi(\\mathcal{C}_{X_K},x_K)\\rightarrow \\pi(\\mathcal{C}_X,x)_K$ is faithfully flat or an isomorphism. 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