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Traditionally, the fully-faithfulness of Riemann-Hilbert correspondance is proved by showing that if M_1 and M_2 are regular holonomic D_X modules, then the canonical morphism of complexes of sheaves RH_{M_1,M_2} : RHom(M_1,M_2) ---> RHom(Sol(M_2),Sol(M_1)) is an isomorphism, in a derived sense. This paper has to do with the converse statement. We prove that if M is an holonomic D_X module for which RH_{M,M} is an isomorphism, then M is regular."},"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":"1401.1618","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-01-08T09:05:22Z","cross_cats_sorted":[],"title_canon_sha256":"00b3da3a3b01e3f11a41e6623820bf8c8aba09bfb2e53e03a75f7480eed45186","abstract_canon_sha256":"5a1134cd2139a2117a79081b395a708b927edd3eb2b2334cf18995e908200cb2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:43.214221Z","signature_b64":"Muy+QvzENXv6lsLN1B5meNNQ3tzH3dAdA3QjrAmB17M3Talt87r6opSAEvnhC4XUSvIkrMPIwSUDjLQYdLZmAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c2ecb959dfc38b170a5d49db926299cad0d967a0653f8a18f0693ad847d4923","last_reissued_at":"2026-05-18T02:57:43.213573Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:43.213573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sur une caract\\'erisation des D-modules holonomes r\\'eguliers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jean-Baptiste Teyssier","submitted_at":"2014-01-08T09:05:22Z","abstract_excerpt":"Let X be a smooth complex manifold. Let Sol denote the solution functor for D-modules on X. Traditionally, the fully-faithfulness of Riemann-Hilbert correspondance is proved by showing that if M_1 and M_2 are regular holonomic D_X modules, then the canonical morphism of complexes of sheaves RH_{M_1,M_2} : RHom(M_1,M_2) ---> RHom(Sol(M_2),Sol(M_1)) is an isomorphism, in a derived sense. This paper has to do with the converse statement. 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