An approach to the Tate conjecture for surfaces over a finite field

Bruno Kahn

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arXiv · 2505.07337

An approach to the Tate conjecture for surfaces over a finite field

Bruno Kahn

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Abstract

We give a reformuation of the Tate conjecture for a surface over a finite field in terms of suitable affine open subsets. We then present three attempts to prove this reformulation, each of them falling short. Interestingly, the last two are related to techniques used in proofs of Gersten's conjecture.

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Bruno Kahn. 2025-05-12. An approach to the Tate conjecture for surfaces over a finite field. https://arxiv.org/abs/2505.07337

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