Brauer groups of abelian varieties over fields of finite characteristic

2025/11/11 by Livia Grammatica, Alexei N. Skorobogatov, Grammatica, Livia +3 · 1 citation
Computer Science · Mathematics · #11G10 #14F22 #14F30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2511.08840

openalex publication_date 2025/11/11 · openalex created_date 2025/11/14 · openalex updated_date 2026/07/28

Abstract

We study the Brauer group of an abelian variety A over an algebraically closed field of characteristic p focusing on the p-primary torsion, the key part of which is a certain quasi-algebraic unipotent group U_A. We determine its dimension and obtain a sharp upper bound for its p-exponent. The isogeny class of U_A is classified for abelian varieties A of dimension at most 3. For principally polarised abelian varieties we compute the dimension of the p-torsion subgroup of U_A in terms of the Ekedahl--Oort type of A.

Citations

• Formal smoothness of the Artin-Mazur formal groups
• Some applications of the Nygaard filtration and quasisyntomic descent in positive characteristic
• Faster computation of Witt vectors over polynomial rings
• Remarks on p-primary torsion of the Brauer group
• Boundedness of the p-primary torsion of the Brauer group of products of varieties
• Absolute prismatic cohomology
• Representability of cohomology of finite flat abelian group schemes
• Topological Hochschild homology and integral p-adic Hodge theory
• Stratifications of Newton polygon strata and Traverso's conjectures for p-divisible groups
• Minimal p-divisible groups

Cited by

• Higher dimensional dominoes in de Rham-Witt cohomology

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• Boundedness of the p-primary torsion of the Brauer group of products of varieties
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• Tate Conjecture and Higher Brauer Groups of Abelian Varieties in Characteristic Zero
• Invariant Brauer group of an abelian variety