Section and towers
Algebraic Geometry
2021-04-13 v1 Logic
Abstract
We discuss the towers of finite \'etale covers which were essentially introduced by A.Tamagawa. The statement about correspondence between sections and cofinal towers is a folklore but perhaps not in a very explicit form. The last section explains how the "injectivity statement" of Grothendieck section conjecture fails for abelian varieties, which is also known in some form. The paper is based on an earlier article which was aimed to reinterpret anabelian setting in model theory terms.
Cite
@article{arxiv.2104.05595,
title = {Section and towers},
author = {Boris Zilber},
journal= {arXiv preprint arXiv:2104.05595},
year = {2021}
}