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Newton polygons as lattice points. (English) Zbl 1057.11506
Summary: Let \(M\) be the reduction modulo \(p\) of a Shimura variety, and let \(N(M)\) be the partially \(N\) ordered set predicted to be the set of all types occurring in the stratification of \(M\) by Newton polygons, in the context of \(F\)-isocrystals with additional structures. We prove that \(N(M)\) is ranked \(N\) (or catenary), in the sense that any two maximal chains have the same length. We also give a Lie-theoretic formula for the distance between two comparable elements in \(N(M)\). This formula can be used to give the expected dimension of the Newton strata of \(M\).

11G18 Arithmetic aspects of modular and Shimura varieties
14G35 Modular and Shimura varieties
14K10 Algebraic moduli of abelian varieties, classification
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