Odd-dimensional cohomology with finite coefficients and roots of unity

Yuri G. Zarhin

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arXiv · 1507.08238

Odd-dimensional cohomology with finite coefficients and roots of unity

Yuri G. Zarhin

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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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Yuri G. Zarhin. 2016-06-01. Odd-dimensional cohomology with finite coefficients and roots of unity. https://arxiv.org/abs/1507.08238

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