Vanishing theorems and Brauer–Hasse–Noether exact sequences for the cohomology of higher-dimensional fields

DOI10.1090/tran/7861zbMath1454.11201arXiv1803.08774OpenAlexW2962959530MaRDI QIDQ5243114

Diego Izquierdo

Publication date: 14 November 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.08774

zbMATH Keywords

Galois cohomologysingularitiesBloch-Kato conjectureHasse principleBrauer group\(p\)-adic base fieldsBrauer-Hasse-Noether exact sequencefinite base fieldsfunction fields in two or more variablesglobal base fieldsLaurent series fields in two or more variables

Mathematics Subject Classification ID

Galois cohomology (11S25) Galois cohomology (12G05) Singularities of surfaces or higher-dimensional varieties (14J17) Finite ground fields in algebraic geometry (14G15) Local ground fields in algebraic geometry (14G20) Varieties over global fields (11G35) Arithmetic ground fields for surfaces or higher-dimensional varieties (14J20) Varieties over finite and local fields (11G25) Global ground fields in algebraic geometry (14G25) Galois cohomology (11R34)

Cites Work

• A finiteness theorem for zero-cycles over \(p\)-adic fields
• Desingularization of two-dimensional schemes
• Cohomologie galoisienne. Cours au Collège de France, 1962--1963. Seconde édition.
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas (Quatrième partie). Rédigé avec la colloboration de J. Dieudonné
• p-Adic Hodge Theory
• Invariants birationnels dans la suite spectrale de Bloch-Ogus
• [https://portal.mardi4nfdi.de/wiki/Publication:5204022 Dualit� et principe local-global pour les anneaux locaux hens�liens de dimension 2 \n (avec un appendice de Jo�l Riou)]
• Hasse principles for higher-dimensional fields
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