On the Newton stratification of a Shimura curve of Hodge type: the case of corestriction

Details On the Newton stratification of a Shimura curve of Hodge type: the case of corestriction On the Newton stratification of a Shimura curve of Hodge type: the case of corestriction

2011-11-25

arxiv.org/abs/1111.5983v1

Mathematics

Algebraic Geometry

47 pages

Scientific paper

This paper studies the Newton stratification of a certain Shimura curve of Hodge type in characteristic $p$. The main results are the determination of the Newton polygons and a mass formula on the cardinality of the supersingular points. The underlying technical results are a direct-tensor decomposition of the associated filtered Dieudonn\'{e} module to a universal abelian scheme over the formal neighborhood of a characteristic $p$ closed point of the integral canonical model of the Shimura curve, and the construction of a so-called weak Hasse-Witt pair by using $p$-adic Hodge theory and relative $p$-adic Hodge theory.

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