2015/09/03 by Xiao Xiao, Xiao, Xiao
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1509.01192
openalex publication_date 2015/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we generalize minimal p-divisible groups defined by Oort to F-crystal over an algebraically closed field of positive characteristic. We prove a structural theorem and give an explicit formula of the Frobenius endomorphism of the isosimple minimal F-crystals that are the building blocks of minimal F-crystals. We then define an invariant called the minimal height for F-crystals using minimal F-crystals and give an upper bound of the isomorphism numbers of isosimple F-crystals in terms of their ranks, Hodge slopes and Newton slopes.