Independence of ℓ-adic Galois representations over function fields

2011/03/15 by Gajda, Wojciech, Petersen, Sebastian
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1103.2893

Abstract

Let K be a finitely generated extension of ℚ. We consider the family of ℓ-adic representations (ℓ varies through the set of all prime numbers) of the absolute Galois group of K, attached to ℓ-adic cohomology of a smooth separated scheme of finite type over K. We prove that the fields cut out from the algebraic closure of K by the kernels of the representations of the family are linearly disjoint over a finite extension of K. This gives a positive answer to a question asked by Serre in 1991.

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