F-isocrystals of Higher Direct Images of p-Divisible Groups

2025/06/13 by Z. Li, Li, Zhenghui, Yanshuai Qin +1
Materials Science · Medicine · #14F22 #14F30 #Algebraic Geometry (math.AG) #Biochemical effects in animals #Enzyme Structure and Function #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2506.11736

openalex publication_date 2025/06/13 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

For a p-divisible group G over a smooth projective variety X over k, where k is a field finitely generated over a perfect field of characteristic p, we show that the formal group Rⁱ f_\fppf* G is isogenous to a p-divisible group. The Dieudonné crystal of its divisible part is canonically isomorphic to the slope-[0,1] part of Rⁱ f_\crys* \cM^cr(G) in the category of F-isocrystals over k. This provides an answer to the rational form of a question of Artin--Mazur regarding the enlarged formal Brauer groups.

Citations

• Representability of cohomology of finite flat abelian group schemes
• On a theorem of Scholze-Weinstein
• Tate Duality In Positive Dimension Over Function Fields
• The p-adic monodromy group of abelian varieties over global function fields of characteristic p
• A comparison theorem for semi-abelian schemes over a smooth curve
• A Variational Tate Conjecture in crystalline cohomology
• Moduli of p-divisible groups

Related

• Logarithmic Dieudonné theory and overconvergent extensions
• Minimal F-crystals and isomorphism numbers of isosimple F-crystals
• Divided Dieudonné crystals
• Weil groups and F-isocrystals
• Overconvergent unit-root F-isocrystals and isotriviality