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arXiv · 1810.06480

A note on the behaviour of the Tate conjecture under finitely generated field extensions

Emiliano Ambrosi
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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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Emiliano Ambrosi. 2018-10-15. A note on the behaviour of the Tate conjecture under finitely generated field extensions. https://doi.org/10.4310/pamq.2018.v14.n3.a4

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