CM-lifts for Isogeny Classes of Shimura F-crystals over Finite Fields

Details CM-lifts for Isogeny Classes of Shimura F-crystals over Finite Fields CM-lifts for Isogeny Classes of Shimura F-crystals over Finite Fields

2003-04-09

arxiv.org/abs/math/0304128v2

Mathematics

Number Theory

71 pages. Preprint from MPI, bonn. Up-dated version to fit submission

Scientific paper

We extend to large contexts pertaining to Shimura varieties of Hodge type a result of Zink on the existence of CM lifts to characteristic 0 of suitable representatives of certain isogeny classes of abelian varieties endowed with endomorphisms over finite fields. These contexts are general enough in order to apply to the Langlands--Rapoport conjecture for all special fibres of characteristic at least 5 of integral canonical models of Shimura varieties of Hodge type.

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