  Over a global field (number field or function field of a curve over a finite
field), theorems for the Galois cohomology of algebraic groups have long been
known. For $F$ the function field of a curve over the formal series field
$\mathbb{C}((t))$, under an additional assumption on the curve, we establish an
explicit description of the localization map in Galois cohomology. This is
achieved by extending the theory of $B(F,G)$ due to Kottwitz.
