Pure and Applied Mathematics Quarterly
Volume 14 (2018)
A note on the behaviour of the Tate conjecture under finitely generated field extensions
Pages: 515 – 527
We show that the $\ell$-adic Tate conjecture for divisors on smooth proper varieties over finitely generated fields of positive characteristic follows from the $\ell$-adic Tate conjecture for divisors on smooth projective surfaces over finite fields. Similar results for cycles of higher codimension are given.
Received 15 October 2018
Published 5 November 2019