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A note on the behaviour of the Tate conjecture under finitely generated field extensions (1810.06480v3)
Published 15 Oct 2018 in math.AG and math.NT
Abstract: 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 co-dimension are given.
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