Galois Cohomology of Reductive Groups over Function Fields over ℂ((t))

2023/12/09 by Dylon Chow, Chow, Dylon
Mathematics · #11E72 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2312.05660

openalex publication_date 2023/12/09 · openalex created_date 2023/12/13 · openalex updated_date 2026/07/28

Abstract

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 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.

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