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We check that the equivalence of categories $sp_{(Y,X),+}$ (from the category of overconvergent isocrystals on $(Y,X)/K$ to that of overcoherent isocrystals on $(Y,X)/K$) commutes with tensor products. Next, in Berthelot's theory of arithmetic $\\mathcal{D}$-modules, we prove the stability under tensor products of the devissability in overconvergent isocryst"},"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":"math/0605125","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2006-05-04T14:50:12Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"21a12967e9a6371df521e80487d09b74eacfa285b1c0c63ea77fe96ab241504b","abstract_canon_sha256":"f821e8d150db23e03af9354cdcfcde7029615c466157bde826dc0ca1d251c64e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:53.415392Z","signature_b64":"hr8H/iFs5lBaDV6kVi+XVeubJqTf6prcKwl0E0pGdqzYbn4b6O7lJQaGndnBrRGKEDPd8a0/Q6VPhAKxcLRgCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a92722b7864f891e432c86b33e86408d19033203825368377b64f58337f30be","last_reissued_at":"2026-05-18T03:39:53.414863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:53.414863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the stability by tensor products of complexes of arithmetic D-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Daniel Caro","submitted_at":"2006-05-04T14:50:12Z","abstract_excerpt":"Let $V$ be a complete discrete valued ring of mixed characteristic $(0,p)$, $K$ its field of fractions, $k$ its residue field which is supposed to be perfect. 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