Dualité et principe local-global pour les tores sur une courbe au-dessus de ℂ((t ))

DOI10.1112/plms/pdv019zbMath1391.11070arXiv1404.4315OpenAlexW1977140606MaRDI QIDQ5256661

Jean-Louis Colliot-Thélène, David Harari

Publication date: 19 June 2015

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.4315

zbMATH Keywords

duality theoremsGalois modulesHasse principle

Mathematics Subject Classification ID

Galois cohomology (12G05) Rational points (14G05) Global ground fields in algebraic geometry (14G25) Galois cohomology of linear algebraic groups (11E72)

Related Items

Duality theorems for function fields over higher local fields ⋮ On the cohomology of reciprocity sheaves ⋮ Weak approximation for homogeneous spaces over some two‐dimensional geometric global fields ⋮ Arithmetics of homogeneous spaces over p$p$‐adic function fields ⋮ Obstructions to weak approximation for reductive groups over \(p\)-adic function fields ⋮ Strong approximation for semi-simple homogenenous groups over the field of functions of a complex algebraic curve ⋮ Abelian varieties for function fields of curves over local fields ⋮ Duality theorem for groups of multiplicative type over some function fields ⋮ Adelic double cosets over semi-global fields ⋮ Local-global principle for function fields over higher local fields. I ⋮ Local-global principles for homogeneous spaces over some two-dimensional geometric global fields ⋮ The adelic space of a torus over a function field ⋮ Local–global principles for curves over semi‐global fields ⋮ Local-global principles for constant reductive groups over semi-global fields ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local-global principles for 1-motives
• Applications of patching to quadratic forms and central simple algebras
• Principal homogeneous spaces under flasque tori; applications
• Patching and local-global principles for homogeneous spaces over function fields of \(p\)-adic curves
• Arithmetic of linear algebraic groups over 2-dimensional geometric fields
• Quasi-abelian crossed modules and nonabelian cohomology
• Cohomologie galoisienne. Cours au Collège de France, 1962--1963. Seconde édition.
• Local-global principles for Galois cohomology
• Unramified Brauer group of homogeneous spaces of tori
• Isotriviality and étale cohomology of Laurent polynomial rings
• Halbeinfache Gruppenschemata über Dedekindringen
• Local-global questions for tori over 𝑝-adic function fields
• Local-global principles for torsors over arithmetic curves
• Weak Approximation for Tori Over p-adic Function Fields
• Global Norm-Residue Map over Quasi-Finite Field