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In his paper, Hesselholt conjectured that $H^1(G,W(\\sO_L))$ is zero, where $\\sO_L$ is the ring of integers of $L$ and $W(\\sO_L)$ is the Witt ring of $\\sO_L$ w.r.t. the prime $p$. He partially proved this conjecture for a large class of extensions. In this paper, we prove Hesselholt's conjecture for all Galois extensions."},"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":"1011.3350","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-15T11:54:39Z","cross_cats_sorted":[],"title_canon_sha256":"7927c807ae983e928aaf82e22637c0d8056d25aa06cb2eb43e2c0655c024bce5","abstract_canon_sha256":"21c69137ec71a1d22df2857292140160303f935190ab4e89c9e425163e863390"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:56.094368Z","signature_b64":"Ffpn4c1uMqoAh3EUVopW1sV61nfuO4SWN/cYq73GmyJt7Kjv6ooK+pY2ISoImAoFhng4tDr1Zr1nlFU+C0HEDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"653976d18e2bd36fa5858ec117572343455926ba88b642c8e067141dcc4935da","last_reissued_at":"2026-05-18T04:35:56.093892Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:56.093892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On cohomology of Witt vectors of algebraic integers and a conjecture of Hesselholt","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Amit Hogadi, Supriya Pisolkar","submitted_at":"2010-11-15T11:54:39Z","abstract_excerpt":"Let $K$ be a complete discrete valued field of characteristic zero with residue field $k_K$ of characteristic $p > 0$. Let $L/K$ be a finite Galois extension with the Galois group $G$ and suppose that the induced extension of residue fields $k_L/k_K$ is separable. In his paper, Hesselholt conjectured that $H^1(G,W(\\sO_L))$ is zero, where $\\sO_L$ is the ring of integers of $L$ and $W(\\sO_L)$ is the Witt ring of $\\sO_L$ w.r.t. the prime $p$. He partially proved this conjecture for a large class of extensions. 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