Log p-divisible groups and semi-stable representations

2023/02/21 by Alessandra Bertapelle, Shanwen Wang, Bertapelle, Alessandra +3 · 2 citations
Mathematics · #11F80 (secondary) #14A21 #14L05 (primary) #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic Geometry (math.AG) #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2302.11030

openalex publication_date 2023/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathscrO_K be a henselian DVR with field of fractions K and residue field of characteristic p>0. Let S denote \mathopSpec \mathscrO_K endowed with the canonical log structure. We show that the generic fiber functor BT_S, d^log→ BT^st_K between the category of dual representable log p-divisible groups over S and the category of p-divisible groups with semistable reduction over K is an equivalence. If \mathscrO_K is further complete with perfect residue field and of mixed characteristic, we show that BT_S, d^log is also equivalent to the category of semistable Galois ℤ_p-representations with Hodge-Tate weights in \0,1\. Finally, we show that the above equivalences respect monodromies.

Cited by

• Logarithmic Dieudonné theory and overconvergent extensions
• Log p-divisible groups associated with semi-abelian degeneration

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