Duality and local- global principle for tori on a curve over C ((t))

作者：Colliot Thelene Jean Louis u^*; Harari David

来源：Proceedings of the London Mathematical Society, 2015, 110(6): 1475-1516.

DOI：10.1112/plms/pdv019

Over a global field K (number field, or function field of a curve over a finite field F), arithmetic duality theorems for the Galois cohomology of tori and finite Galois modules have long been known. More recent work investigates the case where K is the function field of a curve over a p-adic field.
For K the function field of a curve over the formal series field F = C((t)), we establish analogous duality theorems. We thus control the obstruction to the local-global principle and to weak approximation for homogeneous spaces of tori.
There are differences with the afore described cases. For example, the Hasse principle need not hold for principal homogeneous spaces of a K-rational torus.

• 出版日期2015-6