Crystalline Hodge cycles and Shimura curves in positive characteristics

2013/11/05 by Jie Xia, Xia, Jie
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1311.0940

21 pages. Comments welcome

arxiv created 2013/11/05 · arxiv updated 2013/11/06

Abstract

In this paper, we seek an appropriate definition for a Shimura curve of Hodge type in positive characteristics, i.e. a characterization of curves in positive characteristics which are reduction of Shimura curve over the complex field. Specifically, we study the liftablity of a curve in moduli space of principally polarized abelian fourfolds over k, char k=p. We show that some conditions on the crystalline Hodge cycles over such a curve imply that this curve can be lifted to a Shimura curve.

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