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We prove that if $X$ admits an endomorphism which is of degree greater than one on the fibers then $E$ splits into a direct sum of line bundles."},"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":"1609.00910","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-04T09:45:10Z","cross_cats_sorted":[],"title_canon_sha256":"cf05b8e72093f81ae52a45b5b43a0c343b786f979fb46172dc1263173f51e961","abstract_canon_sha256":"5b0749c03bd8cc103fbd092db6f3d77bbc6678929148ca8111ab88b1e91316bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:19.583998Z","signature_b64":"uVvDSMMBduCwzFOpqBfd5mejsEJ38Zflnmf9BOKWdb8LI3GiNJKg5er5QKn6lsnIwD1ux4YD/pGRhH1458ojCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4147fcaa1aeac836f5d1a657f32d71988454925819df4968e6076cb490276e24","last_reissued_at":"2026-05-18T01:06:19.583389Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:19.583389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Endomorphisms of projective bundles over a certain class of varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alexandra Kuznetsova, Ekaterina Amerik","submitted_at":"2016-09-04T09:45:10Z","abstract_excerpt":"Let $B$ be a simply-connected projective variety such that the first cohomology groups of all line bundles on $B$ are zero. 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