On the Tate conjecture for divisors on varieties with h^2,0 = 1 in positive characteristics

2022/07/25 by Paul Hamacher, Hamacher, Paul, Ziquan Yang +3
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2207.11904

openalex publication_date 2022/07/25 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We prove that the Tate conjecture for divisors is ''generically true'' for mod p reductions of complex projective varieties with h^{2, 0} = 1, under a mild assumption on moduli. By refining this general result, we establish a new case of the BSD conjecture over global function fields, and the Tate conjecture for a class of general type surfaces of geometric genus 1.

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