A Characterization of Mumford Curves with Good Reduction
Jie Xia
TL;DR
This paper investigates the good reduction properties of Mumford's Shimura curves of Hodge type in positive characteristic, providing a characterization in the case where the curves are generically ordinary.
Contribution
It offers a new characterization of Mumford curves with good reduction in positive characteristic, specifically in the generically ordinary case.
Findings
Characterization of Mumford curves with good reduction in positive characteristic
Conditions for good reduction in the generically ordinary case
Insights into the reduction behavior of Shimura curves of Hodge type
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds