A Characterization of Mumford Curves with Good Reduction

2013/06/02 by Jie Xia, Xia, Jie
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG

paper · pdf · doi:10.48550/arxiv.1306.0163

18 pages. Comments welcome

arxiv created 2013/06/02 · openalex publication_date 2013/06/02 · arxiv updated 2013/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Mumford defines a certain type of Shimura curves of Hodge type, parameterizing polarized complex abelian fourfolds. In this paper, we study the good reduction of such a curve in positive characteristic and give a characterization in the generically ordinary case.

Citations

• On the Newton polygons of abelian varieties of Mumford's type
• l-adic Monodromy and Shimura curves in positive characteristics

Related

• Tensor decomposition of isocrystals characterizes Mumford curves
• Crystalline Hodge cycles and Shimura curves in positive characteristics
• l-adic Monodromy and Shimura curves in positive characteristics
• Mumford-type Shimura curves contained in the Torelli locus
• Constructing a CM Mumford fourfold from Shioda's fourfold