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In particular when $\\varphi_1$ is a model map too we show that $P$ is still a model of the generic fibre of $G$. We also provide a short proof for the existence of cokernels and quotients of finite and flat group schemes over any Dedekind ring."},"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":"1204.1913","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-09T16:03:44Z","cross_cats_sorted":[],"title_canon_sha256":"a474da1390de6c04bd647015648a8ce021a48cd5ff75587a8e228a1c990dc59b","abstract_canon_sha256":"f437bc58ca129cdfa5a09e9d09294316868cf24938218a55c9dcf610575f0e1d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:22.959958Z","signature_b64":"GXavjSW/nOIGuJGH6454hhf87b/PEOhnKZ4zXZz3hUfeNE7Q2x0aJx7RrgNIpqKORTXK8g7WeiIXbBB0ID8qBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9aa2b409388a65ab0a7dceb572c67f0bcd4515277cfb9cf409ea14f19b430d45","last_reissued_at":"2026-05-18T03:45:22.959353Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:22.959353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pushout of quasi-finite and flat group schemes over a Dedekind ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Marco Antei","submitted_at":"2012-04-09T16:03:44Z","abstract_excerpt":"Let $G$, $G_1$ and $G_2$ be quasi-finite and flat group schemes over a complete discrete valuation ring $R$, $\\varphi_1:G\\to G_1$ any morphism of $R$-group schemes and $\\varphi_2:G\\to G_2$ a model map. 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