Tate Conjecture and Higher Brauer Groups of Abelian Varieties in Characteristic Zero

2016/06/24 by Thomas Jahn, Jahn, Thomas
Mathematics · #11G05 (Secondary) #14C25 (Primary) #14F22 #14G25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1606.07714

openalex publication_date 2016/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be an abelian variety over a field finitely generated over ℚ. We show that the finiteness of the ℓ-primary torsion subgroup of the higher Brauer group is a sufficient criterion for the Tate conjecture to hold. Furthermore, we extend methods for computations of transcendental Brauer groups to higher Brauer groups.

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