On the Cartier duality of certain finite group schemes of order pⁿ, III

2021/05/13 by Michio Amano, Amano, Michio
Mathematics · #14L15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2105.06243

openalex publication_date 2021/05/13 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

Let G^(λ) be a group scheme which deforms \mathbbG_a to \mathbbG_m. We explicitly describe the Cartier dual of the l-th Frobenius type kernel N_l of the group scheme E^(λ,μ;D) which is an extension of G^(λ) by G^(μ). Here we assume that the base ring A is a ℤ_(p)-algebra containing some nilpotent elements. The obtained result generalizes a previous result by N. Aki and M. Amano (Tsukuba J.Math. 34 (2010)) which assumes that A is an \mathbbF_p-algebra.

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