Arithmetic on two dimensional local rings

DOI10.1007/BF01389096zbMath0609.13003OpenAlexW2072435946MaRDI QIDQ1086628

Shuji Saito

Publication date: 1986

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143374

zbMATH Keywords

dualityPicard groupBrauer groupHenselian two-dimensional local field

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Brauer groups of schemes (14F22) Valued fields (12J10) Henselian rings (13J15)

Related Items (24)

On Tate duality for Jacobian varieties. ⋮ Cyclic length in the Brauer group of a p-adic elliptic curve ⋮ Hasse's norm theorem for \(K_ 2\) ⋮ Artin-Verdier duality for arithmetic surfaces ⋮ On the Iwasawa algebra for pro-\(l\) Galois groups ⋮ Unnamed Item ⋮ Arithmetic duality for two-dimensional local rings with perfect residue field ⋮ COMPARING THE BRAUER GROUP TO THE TATE–SHAFAREVICH GROUP ⋮ Finite generation of nilpotent quotients of fundamental groups of punctured spectra ⋮ HASSE PRINCIPLES FOR ÉTALE MOTIVIC COHOMOLOGY ⋮ Indecomposability and cyclicity in the p-primary part of the Brauer group of a p-adic curve ⋮ Some observations on motivic cohomology of arithmetic schemes ⋮ Le théorème de Tate-Poitou pour les corps de fonctions des courbes définies sur les corps locaux de dimension N. (The Tate-Poitou theorem for function fields of curves defined over local fields of dimension N) ⋮ A relative Lubin-Tate theorem via higher formal geometry ⋮ On the \(p\)-dimension of fields ⋮ Toward equivariant Iwasawa theory. II. ⋮ A Hasse principle for function fields over PAC fields ⋮ p-adic étale Tate twists and arithmetic duality☆ ⋮ Log smooth curves over discrete valuation rings ⋮ The cuspidalisation of sections of arithmetic fundamental groups. II ⋮ A note on Gersten's conjecture for étale cohomology over two-dimensional Henselian regular local rings ⋮ Pro-Pgalois groups of function fields over local fields ⋮ Brauer groups of curves and unramified central simple algebras over their function fields ⋮ Hasse's norm theorem for \(K_ 2\)

Cites Work

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• Class field theory for curves over local fields
• Die Approximationseigenschaft lokaler Ringe
• Unramified class field theory of arithmetical surfaces
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• Cohomology of artinian group schemes over local fields
• Lectures on minimal models and birational transformations of two dimensional schemes
• Algebraic approximation of structures over complete local rings
• Duality theorems for curves over p-adic fields
• A Class of 2-Dimensional Local Rings with Artin's Approximation Property
• Complexe de de\thinspace Rham-Witt et cohomologie cristalline
• Rational points in Henselian discrete valuation rings

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