%0 Journal Article %T CM-lifts for Isogeny Classes of Shimura F-crystals over Finite Fields %A Adrian Vasiu %J Mathematics %D 2003 %I arXiv %X 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. %U http://arxiv.org/abs/math/0304128v3