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It is known that $\\Omega$ carries a natural filtration and $\\text{gr} \\Omega=S(\\frak{g})$ where $\\frak{g}$ is the (abelian) Lie algebra of $G$ over $k$. One of our main results in this paper is that the Koszul dual $\\text{gr} \\Omega^!=\\bigwedge \\frak{g}^{\\vee}$ can be promoted to an $A_{\\inf"},"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":"1902.09632","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-02-25T21:52:12Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"7b36a827a4ae2435a545401b8a76746d94059ede03d07498acc370d870158990","abstract_canon_sha256":"e2a0c712a42533d297c6fc98d555156a788abff8375fce7b83c116ae207c0e5e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:35.709984Z","signature_b64":"FQ8Pct751LtpiiOBfEslwEv4ME70Mu3cvvZWvarZE3iwG4jBbt1bh55d+4bdGE1dzovlJvPStUDP2NUAKIUEAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89febf8640086066eaaa27a362e8904022d21698adaa55bc96cc6c99b63da11d","last_reissued_at":"2026-05-17T23:52:35.709397Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:35.709397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Koszul duality for Iwasawa algebras modulo p","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Claus Sorensen","submitted_at":"2019-02-25T21:52:12Z","abstract_excerpt":"In this article we establish a version of Koszul duality for filtered rings arising from $p$-adic Lie groups. 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