Submission date: 12 April 2021

Abstract:

We discuss the towers of finite étale 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.

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Full text arXiv 2104.05595: pdf, ps.