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

2025/05/12 by Bruno Kahn, Kahn, Bruno
Computer Science · Mathematics · #14C25 #19F27 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2505.07337

openalex publication_date 2025/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A Variational Tate Conjecture in crystalline cohomology
• Éléments de géométrie algébrique : IV. Étude locale des schémas et des morphismes de schémas, Quatrième partie

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