2010/09/13 by Mohammad Hadi Hedayatzadeh, Hedayatzadeh, Mohammad Hadi
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1009.2460
openalex publication_date 2010/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \CO be the ring of integers of a non-Archimedean local field and π a fixed uniformizer of \CO . We establish three main results. The first one states that the exterior powers of a π-divisible \CO -module scheme of dimension at most 1 over a field exist and commute with algebraic field extensions. The second one states that the exterior powers of a p-divisible group of dimension at most 1 over arbitrary base exist and commute with arbitrary base change. The third one states that when \CO has characteristic zero, then the exterior powers of π-divisible groups with scalar \CO -action and dimension at most 1 over a locally Noetherian base scheme exist and commute with arbitrary base change. We also calculate the height and dimension of the exterior powers in terms of the height of the given p-divisible group or π-divisible \CO -module scheme.