A note on the behaviour of the Tate conjecture under finitely generated field extensions
Algebraic Geometry
2021-05-11 v3 Number Theory
Abstract
We show that the -adic Tate conjecture for divisors on smooth proper varieties over finitely generated fields of positive characteristic follows from the -adic Tate conjecture for divisors on smooth projective surfaces over finite fields. Similar results for cycles of higher co-dimension are given.
Keywords
Cite
@article{arxiv.1810.06480,
title = {A note on the behaviour of the Tate conjecture under finitely generated field extensions},
author = {Emiliano Ambrosi},
journal= {arXiv preprint arXiv:1810.06480},
year = {2021}
}
Comments
v1:6 pages. Comments are welcome. v2: Corrected a gap in the proof of Theorem 1.1.2. Changed Proposition 3.1.2 accordingly. v3: final version