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

Adrian Vasiu

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

Number Theory 2012-10-25 v3 Algebraic Geometry

Authors: Adrian Vasiu

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.

Keywords

cm-lifts isogeny classes shimura f-crystals finite fields shimura varieties abelian varieties complex multiplication

Cite

@article{arxiv.math/0304128,
  title  = {CM-lifts for Isogeny Classes of Shimura F-crystals over Finite Fields},
  author = {Adrian Vasiu},
  journal= {arXiv preprint arXiv:math/0304128},
  year   = {2012}
}

Comments

Shorter version 62 pages

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