Odd-dimensional cohomology with finite coefficients and roots of unity
Algebraic Geometry
2016-06-02 v3 Number Theory
Abstract
We prove that the triviality of the Galois action on the suitably twisted odd-dimensional \'etale 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.
Keywords
Cite
@article{arxiv.1507.08238,
title = {Odd-dimensional cohomology with finite coefficients and roots of unity},
author = {Yuri G. Zarhin},
journal= {arXiv preprint arXiv:1507.08238},
year = {2016}
}
Comments
10 pages