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

Adrian Vasiu
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Abstract

We extend to large contexts pertaining to Shimura varieties of Hodge type a result of Zink on the existence of lifts to characteristic 0 of suitable representatives of certain isogeny classes of abelian varieties endowed with Frobenius and other endomorphisms over $\dbF_{p^q}$, whose $p$-divisible groups in mixed characteristic $(0,p)$ are with complex multiplication.

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Adrian Vasiu. 2012-10-24. CM-lifts for Isogeny Classes of Shimura F-crystals over Finite Fields. https://arxiv.org/abs/math/0304128

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