p-adic Monodromy of the Universal Deformation of a HW-cyclic Barsotti-Tate Group

2007/08/15 by Yichao Tian, Tian, Yichao
Mathematics · #14F35 #14G32 #14L05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14F35 #msc:14G32 #msc:14L05

paper · pdf · doi:10.48550/arxiv.0708.2022

36 pages, part of the author's thesis

openalex publication_date 2007/08/15 · arxiv created 2008/08/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be an algebraically closed field of characteristic p>0, and G₀ be a Barsotti-Tate group (or p-divisible group) over k. We denote by S the "algebraic" local moduli in characteristic p of G₀, by G the universal deformation of G₀ over S, and by U⊂ S the ordinary locus of G. The etale part of G over U gives rise to a monodromy representation ρ of the fundamental group of U on the Tate module of G. Motivated by a famous theorem of Igusa, we prove in this article that ρ is surjective if G₀ is connected and HW-cyclic. This latter condition is equivalent to that Oort's a-number of G₀ equals 1, and it is satisfied by all connected one-dimensional Barsotti-Tate groups over k.

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