Odd-dimensional cohomology with finite coefficients and roots of unity

2015/07/29 by Zarhin, Yuri G. · 1 citation
#11G10 #14F20 #14K15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1507.08238

Abstract

We prove that the triviality of the Galois action on the suitably twisted odd-dimensional étale cohomogy group of a smooth projective varietiy with finite coefficients implies the existence of certain primitive roots of unity in the field of definition of the variety. This text was inspired by an exercise in Serre's Lectures on the Mordell--Weil theorem.

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