Galois Cohomology of Reductive Groups over Function Fields over $\mathbb{C}((t))$

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.